Turn your 8-quart Instant Pot to the sauté feature. Check your manufacturer’s guide on how to use your Instant Pot model. Pour in olive oil, ground beef and Italian sausage. Cook meat until browned, stirring frequently. Drain excess fat if desired. Season with salt and pepper.
Add the onions and peppers and continue sauteing for 2-3 minutes, or until slightly tender. Add in the mushrooms and garlic. Sauté for 1-2 minutes or until fragrant.
Add to the pot the seasonings, cans of tomato sauce, diced tomatoes, and paste. Stir together.
Cook on High Pressure for 8 minutes. Once cooking time has finished, carefully release the pressure switch. Open Instant Pot lid and stir sauce. Alternatively, you can allow the pressure to naturally release and leave on the keep warm feature until ready to serve.
Season with additional salt and pepper if desired. Serve over fresh pasta and top with the 2 cheeses.