01 - Preheat a grill to medium-high heat, approximately 375 to 400 degrees Fahrenheit.
02 - Brush the halved tomatoes, onion slices, and bell pepper with 1 tablespoon of olive oil, coating evenly.
03 - Place sausages and oiled vegetables on the grill. Cook sausages for 10 to 12 minutes, turning occasionally, until evenly charred and cooked through to an internal temperature of 160 degrees Fahrenheit. 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 grilled tomatoes, onion, and bell pepper.
05 - In a skillet over medium heat, add the remaining 1 tablespoon of olive oil and minced garlic. 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 often, until flavors meld. Stir in the fresh basil and parsley.
06 - Split grinder rolls lengthwise without cutting all the way through. Toast the cut sides on the grill for 1 to 2 minutes until lightly crisp.
07 - Place one cooked sausage into each toasted roll. Spoon the grilled tomato sauce generously over each sausage. Top with shredded cheese if desired.
08 - Return the assembled grinders to the grill over indirect heat, cover, and cook for 1 to 2 minutes until the cheese melts. Serve hot, garnished with extra fresh basil if desired.