Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add olive oil, celery, carrot, onion, and garlic. Cook for 5 minutes, stirring occasionally.
Stir in vegetable broth, diced and crushed tomatoes, tomato paste, basil, salt, and pepper. Close and lock the lid. Select high pressure according to manufacturer’s instructions; set timer for 6 minutes. Allow 10 to 15 minutes for pressure to build.
Meanwhile, melt butter in a small saucepan over low heat. Stir in flour until a smooth, thick paste forms, about 3 minutes.
Release pressure naturally for 2 minutes according to manufacturer’s instructions. Release remaining pressure by opening the valve to vent.
Use an immersion blender to carefully puree the hot soup. Select Saute function again; set timer for 3 minutes. Add flour paste, stirring continuously. Add milk, Parmesan cheese, sugar, and red pepper flakes. Season with more salt and pepper if needed. Stir to combine until the timer ends.
The cane sugar helps cut the acidity, but you can leave it out.
You can use a regular blender to puree the soup. The soup will be extremely hot, so work in batches and be careful when blending.
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