In general, vegetables benefit from a direct, high-heat grilling method. The exceptions are dense root vegetables, like potatoes and turnips, that are best grilled by the indirect method or parboiled and finished over the fire.
ASPARAGUS, OKRA, GREEN BEANS, AND OTHER LONG, SKINNY, FIBROUS VEGETABLES: Snap or cut the ends off the vegetables and arrange four to six vegetables side by side on a work surface. Skewer the vegetables crosswise with slender bamboo skewers, then brush them with olive oil or sesame oil and sprinkle them with salt and pepper. Grill the vegetables over high heat until nicely browned on both sides. Asparagus will take 6 to 8 minutes in all. Okra and green beans will be done in 8 to 10 minutes. Scallions need a total grilling time of 4 to 8 minutes.
CORN: The are two schools of thought on this one. The easiest way to grill corn is simply to toss unshucked ears on the grate and cook them over high heat until the husks are completely charred. Then, you scrape off the charred husks with paper towels (the silk will come off with the husks). It will take 15 to 20 minutes in all for the corn to grill and the result will be sweet and mildly smoky.
My favorite way to grill corn is to start with ears that have the husks pulled back to use as a handle and the silk removed. I generously brush them with melted butter or olive oil and equally generously season with salt and pepper and maybe a little chopped parsley. I grill the corn over high heat, directly over the flames, until the kernels are darkly browned and starting to pop. This takes 8 to 12 minutes in all.
EGGPLANTS: Choose eggplants that are long and slender. Grill the eggplant over high heat until the skin is black and charred on all sides and the flesh is soft; test it by gently poking the top. You’re supposed to burn the skin; that’s what gives the eggplant its smoky flavor. Turn the eggplant with tongs as it cooks: The whole process will take 20 to 30 minutes. Transfer the grilled eggplant to a plate and let cool, then scrape off the charred skin (you don’t have to remove all the burnt pieces; they add terrific flavor). The eggplant is now ready for chopping to make salads or pureeing to make dips.
MUSHROOMS: Mushrooms tend to get somewhat dry if you grill them plain, so it’s best to marinate them for a few hours in an oil-based marinade or slather them with an herb or flavored butter as they grill. For easy grilling and turning, thread small, flat mushrooms on skewers so that they will lie flat on the grill grate (across the cap, not the stem). Larger mushrooms can be sliced or quartered and skewered. Grill mushrooms over high heat, cooking them 3 to 6 minutes per side (6 to 12 minutes in all).
When grilling portobellos, cook them gill side down first, then turn them. Portobellos will be done after 4 to 6 minutes per side (8 to 12 minutes in all). Stuffed mushroom caps should be grilled rounded side down, using the indirect method (with grill covered), for 15 to 20 minutes. Generously baste all mushrooms as they cook.
ONIONS: Cut onions in quarters, but leave the root intact on each piece. Peel the skin back to the root end (the root holds the onion together as it grills) and brush the onion quarters with oil or melted butter. Grill onions over a high flame until they are nicely charred on the outside and cooked through, turning them to ensure even cooking. You’ll need 10 to 12 minutes in all. Cut the root off the onions and scrape away the burnt skin before serving. You can also grill onion slices.
PEPPERS: This method works well for both bell peppers and chile peppers—chose peppers that are rotund and smooth, with relatively few depressions or crevasses. Preheat the grill to high. Place the whole peppers on the grill and cook until darkly charred on all sides, 4 to 5 minutes per side (16 to 20 minutes in all) for larger peppers; smaller chiles will take less time. Don’t forget to grill the tops and bottoms of the peppers; if necessary, hold the peppers with tongs if they won’t balance properly on either end. This is another vegetable you’re supposed to burn. Transfer the grilled peppers to a large bowl and cover it with plastic wrap or place the grilled peppers in a paper or plastic bag and close it. This creates steam, which makes it easy to remove the skin. When the peppers is cool enough to handle, scrape the skin off with a paring knife. Cut out the stem and remove the seeds.
Another way to grill peppers is to brush them lightly with olive oil and grill them until they are nicely browned but not burnt. In this case, you won’t have to bother peeling the peppers.
LEAFY VEGETABLES: Cut radicchio in quarters, wedges, or thick slices. Grill kale leaves whole. Grill other leafy vegetables over high heat until the leaves start to brown, 2 to 4 minutes per side. Watch them carefully—do not allow the leaves to burn to a crisp.
TOMATOES: Thread small tomatoes or plum tomatoes in wide, flat skewers and grill them over high heat, turning until the skins are browned and blistered all over. Grill individual tomatoes the same way, turning them with tongs. To grill really large tomatoes (such as beefsteaks), cut them crosswise into 1-inch-thick slices. Brush the tomato slices with olive oil, season them with salt and pepper, and grill over high heat. Small tomatoes and plum tomatoes will be done in 8 to 12 minutes in all. Larger, whole tomatoes take twice as long, and tomato slices take 2 to 4 minutes per side.
ZUCCHINI AND SUMMER SQUASH: Cut the squash lengthwise into 1/4- or 1/2-inch thick slices. Brush each side with olive oil or walnut oil. Season the squash with salt and pepper and grill over high heat. It will be done after 4 to 6 minutes per side.