For the best results, rub the vegetables with vegetable oil or toss them with a clear or light marinade prior to grilling.
Although some cooks prepare corn for the grill by soaking it in its husk and grilling it cloaked, this method steams the vegetable rather than grilling it. For the smoky flavor typical of grilled foods, husk the ears and cook them directly on the grill rack.
Eggplant can be cut lengthwise or crosswise into 1/2-inch-thick slices.
Red, purple, orange, white, yellow, and green peppers are tasty when grilled. Add them to appetizers, sandwiches, and home-baked breads and pizzas as well as salads.
Potatoes can be cooked whole or cut into halves, thick slices, or wedges. To reduce grilling time, blanch cut potatoes for 10 to 15 minutes before grilling.
Summer squash, including zucchini, yellow squash, and pattypan, can be cut into chunks and used for kabobs. You can also slice them lengthwise.
Select firm ripe tomatoes or plum tomatoes for grilling. Cherry tomatoes are easily cooked on skewers.
To prevent onion slices or wedges from falling through the grill rack, cut a large onion into 1/2-inch-thick slices or inch-wide wedges, then push a small metal or water-soaked bamboo skewer through the onion sections to secure them.
To roast peppers, put whole peppers on the grill over medium heat for 15 to 20 minutes, turning occasionally until skin is charred on all sides. Put the peppers in a brown bag, fold over the top to seal, and cool for about 15 minutes. Then cut peppers lengthwise in half and discard stems and seeds; place cut-side down on work surface and scrape off skin with a small knife.
To roast portabello mushrooms, brush with olive oil and grill 4 to 5 minutes each side.
Asparagus: Break off and discard tough asparagus ends. Blanch tips in a large pot of boiling salted water for a minute or two (depending on size), just to remove the raw taste. Drain and transfer to ice water to stop the cooking. Drain again and pat dry. Roll in olive oil. Sprinkle with kosher salt. Cook directly over hot coals, turning the asparagus with tongs as they color, until they are lightly blistered by the grill and hot throughout, about 2 minutes.
Carrots: Leave skinny carrots whole. If carrots are thick at the top and thin on the bottom, cut them in sections and halve the thick ends. Roll carrots in olive oil and season with salt and pepper. Grill over indirect heat until softened, about 20 minutes, moving them progressively closer to the coals.
Potatoes: Roll whole red potatoes, about 1 1/2 inches in diameter, in olive oil. Season with salt and pepper. Grill over indirect heat until the potatoes can be pierced easily, 30 to 40 minutes, moving them progressively closer to the coals.
Sweet potatoes: Grill large, whole sweet potatoes directly on ash-covered coals (not on the grate). Mound some of the coals around the sweet potatoes. Give them a quarter-turn about every 15 minutes so the skin chars evenly. Keep vents partially closed and grill covered so fire does not get too hot. Sweet potatoes weighing about a pound will take 45 to 50 minutes. Split in half and serve with butter.