Preheat oven to 350 degrees F. Grease a 9-inch deep glass dish pie plate with 1 tablespoon olive oil.
In a blender, combine milk, eggs, baking mix, 1 teaspoon salt, and 3/4 teaspoon pepper. Blend until smooth. Add parsley and blend just to combine.
Sprinkle cheddar in an even layer on bottom of pie plate. Top with zucchini, broccoli, and scallions. Pour egg mixture over vegetables. Top with tomatoes and drizzle with remaining 2 tablespoons olive oil. Transfer to oven.
Bake until quiche is puffed and golden brown and bottom of quiche look baked about 1 hour. Remove and let cool, 15 minutes, before slicing into wedges.