Grilled vegetable towers with wilted greens and prosciutto pine nut vinaigrette

3/4 cup olive oil, divided
1 teaspoon coarse sea salt or kosher salt freshly ground black pepper
1 red bell pepper, cored, seeded and cut into 2 large, flat pieces
1 yellow bell pepper, cored, seeded and cut into 2 large, flat pieces
1 small eggplant, sliced crosswise into 1/4-inch slices
1 small zucchini, ends trimmed and sliced lengthwise into 1/8-inch slices
2 large shitake or oyster mushrooms
4 ounces goat cheese, crumbled
1 thick slice prosciutto (about 1/16 lb.), finely chopped
1/3 cup chopped green onions
2 tablespoons pine nuts
1 tablespoon sherry or balsamic vinegar
1/4 teaspoon salt
freshly ground black pepper
pinch of sugar

1. Turn grill to high and preheat for 5 minutes. Combine 1/2 cup olive oil with the coarse salt and 12 to 15 grindings of black pepper on a dinner plate or shallow bowl.
2. Dip both sides of the vegetables in the olive oil mixture as you place on the grill. Reduce grill setting to medium high and grill vegetables 2 to 3 minutes per side. Remove vegetables from grill as they are done.
3. While the vegetables are grilling, combine the prosciutto, green onion and pine nuts with the remaining 1/4 cup of olive oil in a small skillet. Saute until the pine nuts are toasted and the onions wilted. Stir in the sherry vinegar, and season with salt, black pepper and a pinch of sugar. Set aside.
4. Assemble towers, layering several vegetables, then topping with some of the crumbled goat cheese, adding more vegetables and more goat cheese. Begin and end with eggplant rounds.
5. Toss the greens with the warm vinaigrette and place around the vegetable towers.