Preheat oven to 375°.
Heat a nonstick skillet over medium heat. Coat pan with cooking spray. Add onion, and cook 5 minutes, stirring frequently. Add garlic; cook 1 minute, stirring constantly. Stir in pepper and salt. Add spinach; cook 2 minutes, stirring frequently. Remove from heat, and cool slightly. Combine egg whites and egg in a medium bowl, stirring with a whisk. Add spinach mixture, parsley, oregano, and milk, stirring to combine.
Place 1 phyllo sheet on a large cutting board or work surface (cover the remaining dough to prevent drying); lightly coat with cooking spray. Repeat layers with remaining phyllo and cooking spray, ending with phyllo. Gently press phyllo layers together. Lightly coat top phyllo sheet with cooking spray. Cut stack lengthwise into 3 (4 1/4-inch-wide) strips, and cut each strip crosswise to form 4 (4 1/2-inch) squares. Carefully place 1 layered square into each of 12 muffin cups coated with cooking spray; gently press squares into pan to form cups. Fan corners of phyllo cups. Lightly coat the corners of each phyllo cup with cooking spray.
Divide the spinach mixture evenly among phyllo cups. Bake at 375° for 15 minutes. Remove from oven; sprinkle evenly with cheese. Loosely cover; bake an additional 3 minutes.