Heat the olive oil in a large nonstick skillet set over medium heat.
Add the onions and cook until tender, about 5 minutes. Add garlic, oregano, salt and pepper, and cook for 1 minute.
Place the roasted red peppers in the bowl of a food processor. Add the onion mixture, vegetable broth and balsamic vinegar. Puree until the mixture is smooth. Transfer the sauce to the large skillet and heat over medium heat.
Cook the gnocchi according to package directions. Drain and add the gnocchi to the sauce, along with the parsley. Stir to combine. Serve with Parmesan cheese and season with additional salt and pepper, if desired.