Select Sauté to preheat the Instant Pot. When hot, add olive oil and onion. Sauté for about 3 minutes until tender. Add the garlic and sauté for 1 minute more. Add roughly 2 tbsp chicken broth and scrape a spoon along the bottom of the pan to remove any stuck-on bits. Add the broccoli, carrots, salt, cauliflower, and the remaining chicken broth.
Close and seal the lid. Cook on high pressure (Manual) for 3 minutes. When the cook time ends, turn off the Instant pot. Use a quick pressure release. When the valve drops, carefully remove the lid.
With an immersion blender, food processor, or blender, puree the soup, leaving it as creamy or as chunky as you like. Return it to the Instant Pot.
Stir in cheddar cheese, Parmesan cheese, milk of choice, red pepper flakes, and black pepper until the cheese has melted. Taste and season with salt and pepper as desired. Enjoy!