If making pesto from scratch, follow my homemade pesto recipe here. If you are looking for a store-bought one, I love Alessi or Gotham Greens. Add sausage ingredients to a bowl and mix until it is thoroughly combined. Form them into 2 patties per sandwich.
Add butter (or alternatively, neutral oil) to a skillet and add patties. Cook about 4 min per side on medium heat. Reduce heat slightly and cover pan with a lid to let the sausage cook completely through about 5 more minutes. An instant-read thermometer inserted into the center should read at least 160 degrees F.
Add a little pesto to the pan on medium heat and spread in an even layer. Crack an egg over pesto and top with grated parmesan cheese. Cook for 2-3. minutes for an over easy egg.
Toast bread and assemble: Add sausage patties, egg and prosciutto and top with a handful of arugula. Close and enjoy!
Bonus add: This sausage breakfast sandwich is great on its own, but if you want to take it up a notch, combine a little yogurt, Calabrian chili crisp (or your favorite hot sauce) and lemon juice for a little creamy spread.