Preheat oven to 350 degrees. Spray a 8 or 9-inch dish with cooking spray or lightly grease with vegetable oil.
Heat olive oil in a large saute pan over medium heat. Add bacon and cook for 3 to 4 minutes until it begins to crisp. Remove bacon from pan, then add onion and red bell pepper to the bacon drippings. Saute for 3-4 minutes, add garlic and red pepper flakes and saute another minute. Return bacon to pan. Add spinach and cook just until spinach starts to wilt. Turn off heat and set aside. Spinach will continue to wilt.
Place Greek yogurt in a large bowl and whisk until smooth. Add eggs, two at a time, whisking after each addition until smooth. Add grated cheese and salt and pepper to taste.
Pour egg mixture into prepared quiche dish. Top with spinach mixture (much of the spinach mixture will sink into the eggs).
Bake in a preheated oven until eggs have set, about 35-40 minutes. Allow to cool for 10 minutes before serving.