Heat 1/4 teaspoon oil in a large nonstick skillet. Add eggplant; sauté 2 minutes. Remove eggplant from pan; set aside. Heat 1/2 teaspoon oil in pan; add zucchini, yellow squash, and bell pepper, sauté 2 minutes. Remove zucchini mixture from pan, and set aside. Heat 1/4 teaspoon oil in pan. Add chopped onion and garlic, and sauté 2 minutes. Stir in tomato; cook 3 minutes. Return eggplant and zucchini mixture to pan, and cook 5 minutes. Remove pan from heat. Stir in basil and the next 5 ingredients (basil through goat cheese).
Preheat oven to 450°.
Place 1 phyllo sheet on a large cutting board or work surface (cover remaining dough to keep from drying); lightly coat with cooking spray. Place another phyllo sheet on top of first sheet; lightly coat with cooking spray. Repeat with 2 more sheets. Cut stack into 4 (4 1/2 x 14-inch) strips crosswise. Spoon about 1/4 cup vegetable mixture onto short end of each stack. Fold the left bottom corner over mixture, forming a triangle; keep folding back and forth into a triangle to end of strip. Repeat with remaining phyllo and vegetable mixture.
Place triangles, seam sides down, on a baking sheet; lightly coat with cooking spray. Bake at 450° for 6 minutes or until golden. Serve warm with gourmet greens.