Preheat the grill to medium heat.
Prep the veggies: Place the sliced peppers & onions in a medium bowl, then toss with the olive oil and ½ teaspoon each salt & ground black pepper. Set aside.
Grill the sausage: Place the sausages directly on the grill grates and grill for 5-7 minutes per side, or until cooked through. Once done cooking, transfer the sausage to a dish or plate and tent in foil to keep them warm. You could also place the sausages on a rack in your grill to keep them warm over indirect heat as the veggies cook.
Grill the veggies: Meanwhile, as the sausage cooks, grill the veggies. Place the veggies in a grill basket over medium heat, and grill for 7-10 minutes, tossing them often, until they are softened and have a nice char.
Assemble the rolls: Place a sausage in each bun or roll. Top with the grilled peppers and onions, 2 tablespoons of the marinara sauce, and a sprinkling of mozzarella cheese. To melt the cheese, you can place the assembled rolls on the grill and cook with indirect medium-high heat for a minute or two. You could also place the rolls under the broiler for 1-2 minutes.
Garnish with fresh basil, if desired and serve warm.