Preheat the oven to 400 degrees. Spray a 9 inch cake pan or 8 x 8 baking dish with cooking spray and set aside.
Place the kielbasa in a medium skillet and cook over medium high heat for 5-7 minutes or until browned. Remove from heat and cool.
Place the peppers, onion, and asparagus in a medium skillet along with 1 teaspoon olive oil. Saute over medium heat for 5 minutes. Allow to cool for 5 minutes.
Pour the kielbasa and vegetables into a large bowl. Add in the garlic cloves.
Add the eggs and egg whites to the bowl and mix until well combined. Add in the thyme, salt, and pepper.
Stir in 3/4 cup cheese and all of the milk. Mix well.
Pour the mixture into the prepared pan. Sprinkle with remaining cheese.
Bake for 35-40 minutes or until the top is brown and the center is firm.
Remove from oven and cool for 5 minutes before cutting and serving.