Prep. Cut the beef cheeks into 2-inch pieces; you can cut them into smaller pieces if you like.
Saute. Set the Instant Pot to Saute setting on Normal. Add olive oil, onions, carrots and celery and cook for 2-3 minutes to soften slightly. Stir a few times.
Add meat & bits: Add diced beef cheeks, herbs, seasonings and garlic and cook for 1-2 minutes, stirring a couple of times. Pour in the wine and stir, then follow by ⅔ cup of water (or beef stock if using). Stir through, scraping the bottom of the pot and press Cancel to stop the saute process. Finally, pour the tomato sauce over the top and spread but don't stir through (to prevent any burning errors, it will sink through during cooking).
Secure and lock the lid. Set to Manual/Pressure Cook on HIGH pressure for 40 minutes. After 3 beeps, the Instant Pot will start building up pressure (should take about 10 minutes) and the cooking will commence. Once the timer goes off, allow the pressure to release naturally.
In the meantime, prepare other sides such as mashed potatoes and vegetables or things you need for one of the other meals. See our ideas above. We love beef cheeks with chopped parsley and lemon zest, also known as gremolata, so you can prepare that as well.
Finish the dish. Open the lid and stir the meat through the sauce. It should be very tender, and easy enough to shred with a fork. You can serve the beef cheeks as they are over mashed potatoes or you can use a potato masher to break down and shred the meat to turn this into a ragu sauce to go over pasta. If you like a thicker sauce, you can stir in a mixture of 1 tablespoon of flour and 3 tablespoons of water (known as a slurry) into the stew while it's hot and it will thicken up.