Preheat a skillet over medium heat and cook the breakfast sausage patties for about 4 minutes per side or until fully cooked. Remove from skillet and set aside.
In a bowl, whisk the eggs with a pinch of salt and black pepper.
Melt butter in the same skillet over medium heat. Pour in the eggs and cook, stirring gently, until scrambled and fully cooked, about 3-4 minutes. Remove from heat.
Toast the English muffin halves until lightly browned.
To assemble each sandwich, place one sausage patty on the bottom half of an English muffin, top with scrambled eggs, then a slice of cheddar cheese, and cover with the top half of the muffin.
Wrap each sandwich tightly in a sheet of parchment paper.
Place the wrapped sandwiches in a single layer on a baking sheet and freeze for at least 2 hours until solid.
Once frozen, transfer the sandwiches to a large freezer-safe resealable bag or airtight container for storage.