01 - Set your grill to medium-high heat, approximately 375°F to 400°F, and allow it to come to temperature with the lid closed.
02 - Brush the halved tomatoes, onion slices, and bell pepper strips evenly with 1 tablespoon of olive oil, coating all surfaces to promote even charring.
03 - Place the sausages and oiled vegetables directly on the grill grate. Cook the sausages for 10 to 12 minutes, turning every few minutes until evenly charred 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 and set aside.
04 - Allow the grilled vegetables to cool briefly, then coarsely chop them into bite-sized pieces, retaining any juices.
05 - Heat 1 tablespoon of olive oil in a skillet over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant. Add the chopped grilled vegetables and season with 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 stir in the fresh basil and parsley.
06 - Split the grinder rolls lengthwise without cutting all the way through. Place them cut-side down on the grill for 1 to 2 minutes until lightly toasted and crisp around the edges.
07 - Place one grilled sausage into each toasted roll. Spoon a generous amount of the grilled tomato sauce over each sausage. If using cheese, sprinkle it on top, then return the assembled grinders to the grill over indirect heat. Cover the grill and cook for 1 to 2 minutes until the cheese melts.
08 - Remove the grinders from the grill and serve immediately while hot. Garnish with additional fresh basil leaves if desired.