Form sausage into 6 large, thin patties (these will shrink in size when cooked)
In a large frying pan, add oil and heat to medium high
Cook sausage patties for about 3-4 minutes on each side until fully done. Set aside
Cook the eggs over-medium (or until the doneness you like) adding salt and pepper. Optional but recommended: Use a circular cookie cutter to help form the shape for the sandwich
Split the english muffins in half for the sandwich and butter al sides. Add to the pan cut side down to toast over low heat. Once that side is toasted, flip to toast the other side
While the other side is toasting, add a cooked sausage patty, slide of cheddar and the cooked egg (in this order) on bottom half of the english muffin
Place lid over the pan until cheese is melted. Turn heat off
Remove the english muffins from pan and spread 1/2 an avocado on the top half
Place the muffin half with the avocado on top of the egg sausage half
Enjoy the delicious breakfast sandwich to kick start your morning!