01 - Set a grill or grill pan to medium-high heat and allow it to reach full temperature before cooking.
02 - Brush the halved tomatoes, onion slices, and bell pepper strips evenly with 1 tablespoon of olive oil, coating all surfaces.
03 - Place the sausages and oiled vegetables on the grill. Cook the sausages for 10 to 12 minutes, turning occasionally, until charred on all sides and cooked through to an internal temperature of 160°F. Grill the vegetables for 4 to 6 minutes until softened and lightly charred, then remove from the grill.
04 - Once the grilled vegetables are cool enough to handle, coarsely chop them into bite-sized pieces and set aside.
05 - Heat the remaining 1 tablespoon of olive oil in a skillet over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant. Stir in the chopped grilled vegetables, kosher salt, black 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 fold in the chopped basil and parsley.
06 - Split each grinder roll lengthwise without cutting all the way through. Place the rolls cut-side 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. If using cheese, sprinkle it on top, then return the assembled grinders to the grill over indirect heat with the lid closed for 1 to 2 minutes until the cheese melts.
08 - Serve the grinders immediately while hot, garnished with additional fresh basil leaves if desired.