Preheat the oven to 350 degrees.
Line two large (18x13 inch) rimmed baking sheet with parchment paper. Spritz lightly with nonstick cooking spray.
On one baking sheet, place the sausage patties.
In a large bowl, whisk together the eggs, milk, salt, and black pepper until well blended.
Pour the egg mixture into the pan and carefully place in the oven.
Bake the eggs and sausage for 20 to 25 minutes or just until the center of the eggs are set and the sausage is cooked through.
Remove from the oven and allow to cool before cutting the eggs into 12 squares.
Assemble the sandwiches by layering with a half of the muffin, egg square, sausage patty, slice of cheddar cheese, and the remaining muffin half.
To Freeze: Wrap each sandwich individually in aluminum foil, waxed paper, or parchment paper and place them in a zip-top freezer bag. Freeze for up to 1 month.
To Reheat: For best results, thaw the sandwiches in the refrigerator overnight. Remove the paper and rewrap in a paper towel. Microwave for 40 to 60 seconds on 50% power. Flip the sandwich and microwave for an additional 10 to 30 seconds or until the sandwich is warmed through. The sandwiches can also be baked in a 350 degree oven for 10 to 15 minutes.