Toss the sliced peppers and onions with 2 tablespoons olive oil and a few generous shakes of Salt Pepper + Three Chiles. Divide the pork sausage into 4 rounds and set aside.
Whisk together the mayo, calabrian chiles, vinegar, lemon juice, and a three finger pinch of salt. Chill while you cook the burgers.
Heat a griddle or large skillet to medium high heat. Cook the peppers and onions first, sauteing until tender and just browned, about 8 minutes. Remove from the pan and set aside. Cook the sausage balls in the same pan, working on at a time if needed. Drop each sausage round on the griddle then flatten with a large flat spatula, cook until crisped and browned, about 4 minutes per side.
Top each sausage patty with some of the sausages and peppers, followed by 1/4 cup of cheese and cover until just melted. Build each burger with a few swipes of the calabrian chile mayo, some fresh basil leaves and a patty with cheese, peppers and onions on each bun.