Heat an outdoor grill to medium-high, approximately 400 to 450°F. Set up a cooler indirect-heat area if your grill allows, and have a disposable aluminum roasting pan or sturdy grill-safe casserole dish ready.

Toss the sliced bell peppers and onion with 2 tablespoons olive oil, the minced garlic, Italian seasoning, kosher salt, and black pepper. Mix thoroughly so the seasoning coats the vegetables.

Place the sausage links directly on the grill. Cook for about 10 to 15 minutes, turning several times, until browned on the outside; they do not need to be fully cooked yet.

Transfer the seasoned peppers and onions to the grill-safe pan. Stir in the slightly drained diced tomatoes and the optional 1/4 cup wine, beer, or chicken broth.

Nestle the browned sausage links into the vegetable mixture and drizzle with the remaining 1 tablespoon olive oil. Cover the pan tightly with aluminum foil.

Place the covered pan over indirect or medium grill heat and cook for 15 to 20 minutes. Carefully stir the vegetables once during cooking, keeping the pan covered afterward so the trapped steam softens the peppers and onions.

Remove the foil for the final 3 to 5 minutes if you want a thicker sauce and additional browning. Check pork sausage with an instant-read thermometer for 160°F, or poultry sausage for 165°F.

Let the casserole rest for 5 minutes, then sprinkle with chopped parsley or basil. Taste the vegetables and sauce, adding more salt if needed, and serve hot with rolls, polenta, pasta, or grilled bread.