Heat the olive oil in the Instant Pot on SAUTE, high heat. Add the chopped onion and cook until the onion is soft and starting to brown, about 4-5 minutes.

While the onion cooks, coarsely chop the cauliflower, including the stems. Add chopped cauliflower, chicken stock, garlic powder, and salt to the Instant Pot and set on MANUAL, HIGH PRESSURE for 5 minutes cooking time. When five minutes is up, use QUICK RELEASE method to release the pressure.

While the cauliflower cooks assemble the grated sharp yellow cheddar, grated sharp white cheddar, half and half, crumbled cooked bacon, canned green chiles, and Green Tabasco Sauce (affiliate link).

When the pressure has released, use an Immersion Blender (affiliate link) to blend the soup right in the pot. (Or use a food processor or blender to puree the cauliflower, being very careful with the hot liquid.) We made it pretty smooth, since you're adding bacon and green chiles for some texture, but leave a few chunks if you prefer.

Turn the Instant Pot to KEEP WARM (or use SAUTE, low heat if you think you'll need more time.) Add the grated sharp yellow cheddar, grated sharp white cheddar, and milk product of your choice, and stir until the cheese is melted.

Then add the crumbled cooked bacon, diced green chiles with juice, and Green Tabasco Sauce (affiliate link) (if using).

Serve hot, with more grated cheese and crumbled bacon to add at the table, plus other toppings as desired.

Heat olive oil in a medium-sized heavy soup pot and cook the onion until it's soft and just starting to brown.

Chop the cauliflower while the onion cooks.

Increase chicken broth to 3 ½ cups for stovetop version. Add chopped cauliflower, chicken broth, garlic powder, and salt and turn the heat to medium-high and cook until mixture is barely starting to boil. Turn heat to medium-low and simmer until the cauliflower is very tender when pierced with a fork, about 20-30 minutes.

Puree the cauliflower with an immersion blender or other utensil as described above. Check the amount of liquid and if the soup seems thin, simmer on low heat for a few minutes more until some of the extra liquid evaporates.

Add the grated cheese and milk product of your choice and stir over low heat until the cheese has melted.

The add the crumbled bacon, diced green chiles, and Green Tabasco Sauce (if using) and stir to combine.

Serve hot, with more crumbled bacon and grated cheese to add at the table, plus other toppings as desired.