In a small bowl mix together ¼ cup mayonnaise, and some hot sauce to taste.
Thinly slice about ½ of a white onion into paper thin rings and set half aside.
Toss the remaining sliced onion in a small bowl with a big pinch of salt, and a few dashes of hot sauce. Stir to combine and let sit to lightly pickle.
Lightly spread both sides of 2 English muffins with some of the mayo/hot sauce mixture and set aside.
Beat 2 large eggs in a medium bowl until no streaks remain, season with salt and pepper.
If using sausage links, cut open and remove the insides of 6 ounces of breakfast sausage, discarding the casings.
Divide the sausage into two piles and form into balls.
Place the two sausage balls on one half of a piece of parchment paper, fold the second half over them and firmly smash down on each ball with the bottom of a heavy skillet to flatten them into about 4”-ish rounds.
Heat a large cast iron skillet over medium heat and toast the English muffins, cut sides down, until golden brown.
Increase the heat to medium high, add 1 tablespoon vegetable oil to the skillet, and arrange both sausage patties in the skillet.
Top each patty with raw sliced onions and season with salt.
Cook until the patties are browned and crisp, then flip them over and place one slice of American cheese on each patty.
Cover the skillet to allow the cheese to melt.
In a small non-stick skillet, heat 1 tablespoon of butter and add the beaten eggs, scrambling until large fluffy curds have set.
Slather more of the spicy mayo on each side of the English muffins.
Assemble the sandos by placing a sausage patty on the bottoms of the muffins, dividing the scrambled eggs among them, adding more hot sauce, marinated onions, arugula, and the tops of the English muffins.
