Some vegetables do require precooking before being turned into shish kebabs for the grill, and some don't need anything but a good wash and dry before you skewer them. Once any veggie is on the grill, cook it until its interior is soft and tender and its exterior is browned and slightly charred. Equally important is cutting the veggies into uniform pieces that can cook for the same amount of time, and being very careful not to allow vegetables to come into contact with any raw meat or poultry.
From the Pot to the Fire
White potatoes, sweet potatoes and winter squash all need precooking before you put them on the grill, to reduce grilling time. Cut the vegetables into 1-inch chunks, peeled or not for the potatoes, and place them in a pot of salted, cold water. Bring the water to a boil, and cook at a rolling boil until the veggies are just tender and can be easily pierced with a paring knife -- about 5 minutes for sweet potatoes and 10 minutes for white potatoes or squash. Grill the kebabs over direct heat for 15 to 20 minutes, turning them regularly.
Boil, Blanch and Grill
Like sweet and white potatoes, baby artichokes and artichoke hearts need parboiling in salted water until they are tender. Remove the inner chokes from the artichokes, and one or two layers of outer leaves, before boiling them for about 10 minutes. After boiling, plunge them into a bowl of ice water to stop them from cooking further. To grill, place the artichoke skewers over direct heat and cook until they're browned and completely tender, about 10 minutes.
Ready in Five
Some veggies don't require precooking and hardly require any time on the grill to cook. Depending on their thickness, skewered asparagus pieces, eggplant chunks and cherry tomatoes may need as little as 5 minutes over direct heat until they're done. Toss the vegetables in oil and sprinkle with salt and pepper before grilling. You'll know they're done if you can pierce them with a knife or skewer.
Give 'Em Time
Broccoli, corn, eggplant, fennel, mushrooms, onions and zucchini can be skewered and placed directly on the grill without precooking. Cut them into similar sized pieces or place them on individual skewers. These veggies take from 10 to 15 minutes to cook over direct heat. You want some charring on the vegetables, but if they start cooking too quickly and become charred before they're tender, move them to the outer edges of the grill and continue cooking over indirect heat.