01 - Set a grill to medium-high heat and allow it to reach full temperature before cooking.
02 - Brush the halved tomatoes, onion slices, and bell pepper with 1 tablespoon of olive oil, coating all sides evenly.
03 - Place sausages and oiled vegetables on the grill together. Cook sausages for 10 to 12 minutes, turning occasionally, until evenly charred and cooked through to an internal temperature of 160°F. Grill vegetables for 4 to 6 minutes until softened and lightly charred.
04 - Remove vegetables from the grill and let cool briefly. Coarsely chop the tomatoes, onion, and bell pepper into uniform pieces.
05 - Heat 1 tablespoon of olive oil in a skillet over medium heat. Add minced garlic and sauté for 1 minute until fragrant. Add the chopped grilled vegetables and season with salt, pepper, dried oregano, and crushed red pepper flakes. Cook for 3 to 4 minutes, stirring frequently, until the flavors meld together. Remove from heat and stir in the fresh basil and parsley.
06 - Split grinder rolls lengthwise without cutting all the way through. Place cut sides down on the grill for 1 to 2 minutes until lightly crisped and golden.
07 - Place one grilled sausage into each toasted roll. Spoon the grilled tomato sauce generously over each sausage. Top with shredded cheese if desired. Return to the grill over indirect heat, cover, and cook for 1 to 2 minutes until the cheese melts.
08 - Serve immediately while hot, garnished with additional fresh basil leaves if desired.