Wash and dry the cauliflower. Chop into 1-2 inch pieces. If roasting, rub with a little olive oil and salt and pepper to taste. Put into the air fryer basket and air fry at 400°F for 10-12 minutes or until cauliflower begins to brown slightly. This can also be done in a standard oven. If not roasting, skip this step.
Put 1 tablespoon of olive oil into the inner pot and set to saute on high for 3 minutes. (If you used the air fryer lid and roasted the garlic in the Instant Pot, leave any bits of cauliflower that fell into the inner pot). When the oil is hot, add diced carrots, celery, and onion. Add minced garlic during the last minute. Stir frequently while cooking.
Turn off saute and pour the vegetable broth into the pot. Deglaze with a wooden spoon to release any stuck pieces of food on the bottom of the pot. Add the cauliflower, lemon juice, salt, pepper, and thyme. Do not stir.
Close and seal the lid. Set to pressure cook/manual on high for 5 minutes. Complete a controlled quick release when finished. Open the lid and stir.
Using an immersion blender, blend the soup until it reaches your desired consistency. Alternatively, put soup into a high speed blender and blend until creamy.
Transfer the inner pot to a heat-proof surface and wait 1 minute. Add the shredded cheese and stir until melted and smooth. Taste and season with additional salt and pepper if desired. If thickening further with a roux, see notes below.
Serve immediately, with your choice of garnishings.