Toss the sausage, peppers, onion and broccoli rabe with about 2 tablespoons olive oil. Grill until the sausage is cooked through and the vegetables are slightly tender and a little charred, 10 to 15 minutes. Slice the sausage, peppers and onions. Cut the broccoli rabe into 1/2-inch pieces.
In a small pot, heat 2 tablespoons oil over medium-low heat. Add the sliced garlic and saute until fragrant but not browned, 1 to 2 minutes. Add the tomato sauce and bring to a simmer. Turn the heat to low and cook for about 5 minutes to allow the garlic to infuse into the tomato sauce.
Remove some of the bread from the inside of each grinder roll. Dress the grinder rolls with about 2 tablespoons olive oil and some salt and pepper. Grill until toasted, 1 to 2 minutes, then rub with a clove of garlic.
In a large bowl, combine the sausage, peppers, onion, broccoli rabe, tomato sauce, pickling liquid from the cherry peppers, oregano and red pepper flakes and season with salt and pepper. Toss until coated.
In a separate bowl, combine the cherry peppers, basil, parsley and red wine vinegar and season with salt and pepper. Add about 2 tablespoons olive oil to bind it all. Mix until well combined.
Place enough of the sausage mixture into each bun to fill. Cover with 2 slices of provolone cheese in each grinder. Place back on the grill on the top rack with the cover down. Cook until the cheese is melted, about 5 minutes. Top with the cherry pepper mixture.