Preheat oven to 375 degrees F. In a large nonstick skillet heat oil over medium-high heat. Add onion and sweet pepper; cook about 4 minutes or just until vegetables are tender. Add zucchini; cook about 4 minutes more or just until zucchini has begun to brown. Add spinach, garlic, and 1/4 teaspoon salt; cook for 2 minutes more.
In a small bowl combine evaporated milk, eggs, 1/4 teaspoon salt, the black pepper, and nutmeg.
Coat a 9-inch pie plate with cooking spray. Unfold phyllo dough; remove one sheet of the phyllo dough. (As you work, cover the remaining phyllo dough with plastic wrap to prevent it from drying out.) Place phyllo dough sheet in prepared pie plate; lightly coat with cooking spray, gently pressing into bottom and up sides of pie plate and letting ends of phyllo sheet hang over edges of pie plate. Repeat with the remaining nine phyllo sheets, placing sheets in a crisscross pattern. Spoon vegetable mixture evenly over phyllo; sprinkle with cheese. Pour egg mixture over all. Fold overlapping ends of phyllo toward center of pie plate. Coat the top of the phyllo with cooking spray; gently press to hold shape.
Bake about 40 minutes or until a knife inserted off center comes out clean. Cool for 15 minutes on a wire rack. Cut into wedges and serve warm.