Preheat the oven to 425°F (220°C). Line a large rimmed baking sheet with foil or parchment for easy cleanup and set aside.
Warm a large skillet over medium-high heat with 1 teaspoon of the olive oil. Brown the sausages on all sides for about 4–5 minutes total — you’re not cooking them through, just building color. Transfer the sausages to the prepared sheet pan and space them out.
In a large bowl, combine the sliced peppers, onion wedges, and sliced garlic. Drizzle with the remaining 1 tablespoon olive oil, sprinkle the dried oregano, kosher salt, and black pepper, then toss with your hands or a spatula until everything is evenly coated.
Spread the seasoned vegetables around and between the sausages on the sheet pan in a single layer so they roast instead of steam.
Roast in the preheated oven for 20 minutes, then use tongs to flip the sausages and stir the vegetables so the pieces at the edges move toward the center. Return to the oven and roast an additional 10–12 minutes, until sausages register 160°F and peppers are tender and slightly charred.
Remove the pan from the oven and drizzle the balsamic vinegar over the hot sausages and peppers. Gently toss everything on the pan to coat and let rest for 5 minutes so juices redistribute.
Slice the sausages on the bias (optional) and serve family-style straight from the sheet pan or over crusty bread, rice, or polenta.