Step 1: Prepare the vegetables: Cut the eggplant, zucchini, and yellow squash lengthwise into 1/4-inch-thick slices. Core, seed, and quarter the bell peppers. Quarter the onion, leaving the root end attached to each piece (the root will help the onion hold together as it grills).

Step 2: Make the basting mixture: Combine the olive oil, lemon juice, and garlic in a small bowl. If using dried rosemary, add it directly to the olive oil mixture.

Step 3: Set up the grill for direct grilling and preheat to high.

Step 4: When ready to cook, brush the eggplant, zucchini, squash, bell pepper, and onion slices with some of the olive oil mixture. using the rosemary sprig as a basting brush. (If you are not using fresh rosemary, use a pastry brush.) Arrange the vegetables on the hot grate and grill, turning with tongs, until nicely browned, 3 to 6 minutes per side. Brush the vegetables once or twice more with the olive oil mixture and season them with salt and black pepper as they cook. Transfer the vegetables to a platter to cool. Cut the root end off the onion wedges and break the layers apart.

Step 5: To serve: Cut the bread crosswise into four equal pieces. Split each piece lengthwise in half for the sandwiches. Brush the insides of each piece of bread with any remaining olive oil mixture and spread the goat cheese over them. Sandwich the eggplant, zucchini, squash, bell pepper, and onion slices inside the bread. Cut the sandwiches in half and serve warm or at room temperature.