Heat a large skillet over medium heat. Cook sausage patties in the hot skillet, turning often, until sausage is cooked through and browned, 10 to 12 minutes. Remove patties to a paper-towel lined plate.
Meanwhile, coat a 3-inch mini frying pan with coconut oil cooking spray and place over medium heat. Whisk 1 egg and 1 dash of cayenne pepper in a small bowl and season with salt and pepper. Pour egg mixture into frying pan. Cook, without stirring, until set on the bottom, about 1 1/2 minutes. Flip egg and cook, without stirring, until set on the other side, about 1 minute more. Remove from heat, place on a plate, and repeat with remaining eggs and cayenne pepper.
Assemble breakfast sandwiches when eggs and sausage are cool: place an egg patty on the bottom piece of an English muffin, top with a slice of cheese, a sausage patty, and the English muffin top. Wrap in aluminum foil and freeze.
Unwrap and microwave each sandwich for 2 minutes when ready to eat.