Heat the oil in a large skillet over medium-high heat. Add the onions and peppers and saute until the onions are translucent and the peppers are tender, 6 to 8 minutes. Stir in the tomato paste and cook for 1 minute longer. Remove from the heat.
Preheat an outdoor grill to medium high.
Combine both sausages in a bowl. Form into 4 patties. Grill until cooked through, 4 to 5 minutes per side. Top each burger with some of the onions and peppers and 2 slices of cheese, cover the grill and cook until the cheese melts.
In a bowl, add the mayo and pesto and stir to combine. Spread the rolls with the pesto mayo, add the burgers and banana peppers and serve immediately.