Put the sausage slices, sliced peppers and onion in a bowl along with the balsamic vinegar, olive oil, kosher salt, pepper, garlic powder, and dried oregano. Toss until combined.
Preheat your grill to medium heat with the grill basket (my grill basket was the kind with an open top, picture in post above).
Add the sausage and veggies to the grill basket. Grill 18 to 22 minutes, carefully tossing everything together a few times with tongs. Serve with goat cheese or feta cheese over top and with basil and balsamic glaze if desired.