Add the tomatoes, onion, carrot, and garlic to your Instant Pot. Sprinkle the oregano, basil, salt, and pepper over the top of the vegetables. No need to stir.
Secure the IP lid and be sure the steam release valve is set to Sealing. Select Manual and cook at high pressure for 20 minutes. Remember, it will take about 10 minutes for the pressure to build in the pot before the cooking cycle actually begins. The IP display will show "On" until pressure is reached.
When the cooking cycle completes, the pot will beep. Set a timer for 10 minutes and allow the pressure to naturally release. When the timer goes off and the display reads L0:10, move the steam release valve to Venting and the remaining pressure will release. Once the pressure is released, remove the lid.
Add your parmesan cheese rind chunks (optional) and put the lid on for the rinds to melt.
In about 10 minutes, use an immersion blender to blend the cooked vegetables into a nice, smooth sauce. Add in the tomato paste and use a whisk to make sure it's fully mixed to thicken the sauce. Adjust any seasoning to taste and you're ready to serve!
This sauce should keep well in an airtight container for up to a week in the fridge, or you can freeze it for up to 3 months