Grilled Vegetables with Rosemary-Goat Cheese Polenta

• 1 Tbsp butter (unsalted)
• 1/2 cup onion, finely chopped 
• 3/4 cup polenta or stone-ground yellow cornmeal
• 1 can (14-ounce) reduced sodium chicken broth (or vegetable broth)
• 1 1/2 tsp coarse salt
• 1 1/2 tsp fresh-ground pepper
• 1/4 tsp cayenne pepper
• 3 Tbsp goat cheese
• 2 Tbsp rosemary, roughly chopped
• 1/2 cup extra-virgin olive oil
• 2 Tbsp extra-virgin olive oil
• 6 pound(s) mixed vegetables such as asparagus, cabbage, Japanese eggplant, summer squash, red potatoes, bell peppers, halved or quartered

1. Make polenta: Line baking pan with plastic wrap and set aside. Melt butter in large, heavy saucepan over medium heat and sauté onion until golden -- about 10 minutes. Stir in polenta, broth, 1/2 teaspoon salt, 1/2 teaspoon black pepper, and cayenne pepper and bring mixture to boil. Lower heat and cook until polenta thickens -- 10 to 15 minutes. Stir in 1 cup water, cheese, and chopped rosemary. Transfer polenta to prepared pan, spread evenly, and cool completely.

2. Grill polenta: Heat a grill until very hot. Invert polenta pan onto clean surface. Cut polenta into 3-inch triangles, brush each with oil, and place on grill. Cook until polenta is heated through and golden -- about 10 minutes. Place grilled polenta triangles on a platter and keep warm.

3. Grill vegetables: Place vegetables in large bowl, add remaining olive oil, salt, and pepper, and toss to coat. Grill vegetables until they just begin to soften. Place grilled vegetables over polenta and serve immediately.