Preheat the oven to 350°F (175°C).
Bake the frozen biscuit dough according to package instructions, about 12-15 minutes, until golden brown. Remove from oven and let cool completely.
While biscuits bake, cook turkey sausage patties in a skillet over medium heat for 4-5 minutes per side until fully cooked and browned. Remove from skillet and set aside.
In a medium bowl, whisk together eggs, whole milk, salt, and black pepper until well combined.
Heat unsalted butter in a nonstick skillet over medium-low heat. Pour in the egg mixture and cook gently, stirring occasionally, until soft scrambled and fully cooked, about 5-7 minutes. Remove from heat.
Once biscuits are cool, slice each biscuit in half horizontally.
Assemble each sandwich by layering scrambled eggs, one turkey sausage patty, and one slice of cheddar cheese between biscuit halves.
Wrap each sandwich tightly in plastic wrap and then in aluminum foil for freezing.
To reheat, remove foil and plastic wrap, wrap sandwich in a paper towel, and microwave on high for 1-2 minutes until heated through. Alternatively, reheat in a 350°F (175°C) oven for 15-20 minutes if thawed.