Set your Instant Pot to the Sauté. Melt 3 tablespoons of butter and add the celery, carrots, onion, and garlic. Sauté for about 5 minutes, stirring now and then.
Pour in chicken broth, along with the fire-roasted tomatoes and San Marzano tomatoes, tomato paste, basil (if using dried), salt, and pepper. Secure the lid and set the cooker to high pressure, following your device’s instructions. Set the timer for 6 minutes. It will take around 10 to 15 minutes for the pressure to build.
While waiting, melt butter in a small saucepan over low heat. Gradually stir in flour to create a smooth, thick paste. This will take around 3 minutes.
After the pressure cooking is complete, allow the pressure to naturally release for 2 minutes. (Naturally release = wait to release.) Carefully release the remaining pressure by opening the vent.
Using an immersion blender, blend the hot soup until smooth. Switch back to the Sauté function and set the timer for 3 minutes. Stir in the flour paste, then add milk, Parmesan, sugar, and crushed cayenne pepper. Taste and adjust seasoning with additional salt and pepper, if needed.