Combine first 6 ingredients in a large bowl, stirring with a whisk until combined; set aside.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add bell pepper and onion; sauté 4 minutes or until tender. Reduce heat to medium. Pour egg mixture into pan; let egg mixture set slightly. Tilt pan; carefully lift edges of omelet with a spatula to allow uncooked portion to flow underneath cooked portion. Cook 3 minutes. Wrap handle of pan with foil; place pan under broiler. Broil 1 minute or until set and lightly browned.
Arrange muffin halves in a single layer on a baking sheet. Sprinkle muffin halves evenly with cheese, and broil 1 minute or until cheese begins to brown.
Divide omelet into 4 portions; place 1 portion on bottom half of each muffin. Top evenly with spinach leaves; top with remaining muffin halves.