Heat 1/4 teaspoon oil in a large nonstick skillet.
Add eggplant; saut 2 minutes.
Remove eggplant from pan; set aside.
Heat 1/2 teaspoon oil in pan; add zucchini, yellow squash, and bell pepper, saut 2 minutes.
Remove zucchini mixture from pan, and set aside.
Heat 1/4 teaspoon oil in pan.
Add chopped onion and garlic, and saut 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 45
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.