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.
Adapted from "Endless Summer" by Katie Lee © Harry N. Abrams 2015. Provided courtesy of Katie Lee. All rights reserved.