1: Prepare the vegetables: Cut the sharp points off the artichoke leaves, if using. Cut the artichoke from crown to stem into 6 wedges. (Cut baby artichokes in half.) Cut out and discard the fibrous choke. Rub the artichoke wedges with cut lemon to keep them from discoloring.

2: Cut the onion from top to bottom into wedges. Pin each crosswise with a toothpick (this keeps the wedges from falling apart).

3: Trim off the ends of the broccolini and separate it into stalks.

4: Lightly brush the artichokes, onion, broccolini, zucchini, snap peas, corn, padrón peppers, and mini bell peppers with olive oil and season with salt and pepper.

5: Meanwhile, set up your grill for direct grilling and build a hot fire. Ideally, you’ll work over a grapevine or orange wood fire. Otherwise, add wood chunks or chips to the coals or place in the smoker box or under the grate directly over the burners of your gas grill. Brush or scrape the grill grate clean and oil it well.

6: Arrange the oiled seasoned vegetables on the grill and grill until darkly browned on all sides, 2 to 4 minutes per side. Don’t worry about cooking them through—they’ll finish cooking in the paella.

7: Transfer the vegetables to a cutting board. Remove the toothpicks from the onions and snap peas. Cut the zucchini into 2-inch pieces. Cut the corn crosswise into 1-inch rounds. The veggies can be grilled and prepped ahead to this stage. Cover and refrigerate for up to 1 day.

8: Place the paella pan over the fire. Add the 2 tablespoons of olive oil and heat until shimmering. Add the diced onion and bell pepper and cook over high heat, stirring with a long-handled implement, like a grill hoe or long-handled wooden spoon, until the onions begin to brown, about 4 minutes. Add the garlic, parsley, diced tomato, and salt and pepper after 2 minutes. If the mixture—called a sofrito—starts to burn, slide the pan to a cooler part of the grill. Note: The Spanish wouldn’t brown the sofrito, but you’ll get more flavor if you do.

9: Stir in the rice and sauté until the grains look shiny, 1 minute. Stir in the soaked saffron (with its liquid) and the wine and boil for 2 minutes.

10: Stir in 6 cups of stock, or more as needed to cover the rice with liquid. Adjust the heat (by moving the paella pan closer or further away from the hot part of the fire) to obtain a gentle simmer. Gently simmer the rice for 10 minutes.

11: Stir in the artichokes, if using and simmer for 5 minutes. Stir in the remaining grilled vegetables and the cherry tomatoes and chickpeas. Continue cooking the paella until the rice is al dente, 20 to 27 minutes in all, stirring occasionally. Add more stock (1/2 cup at a time) as needed. Add salt and pepper to taste: The paella should be highly seasoned.

12: If you get it right, all the liquid will cook out and the bottom of the rice will turn into a crisp savory crust called soccarat. Serve the paella straight from the pan.