Remove english muffins from freezer and allow them to thaw on countertop. Once thawed, toast to desired doneness.
In a small bowl, whisk egg and milk.
Place a medium fry pan over medium heat and add 1 tbsp butter
Add sausage patty and cook for a few minute on each side until warmed through. Remove from pan.
Add eggs and stir constantly on low heat until eggs start to set up. When the eggs are almost all the way cooked, add the slice of cheddar cheese and cover with lid.
Build sandwich: place bottom half of english muffin down on place, place sausage patty on english muffin, then eggs, then top with the second half of the english muffin