Place the Instant Pot or other pressure cooker in saute mode. Melt the butter and add the diced sweet onions. Cook until translucent, stirring occasionally, about 3 - 4 minutes. Add the garlic and stir for another minute, until fragrant (do not burn the garlic!).
Stir in the chicken broth and let it come back up to heat, another 2 minutes or so.
Add the potatoes, cauliflower, thyme, bay leaf, and mustard.
Cook on high pressure for 10 minutes. Quick release the pressure (careful not not to stand over the pot as the steam can cause burns).
(OPTIONAL) In a separate pan prepare the bacon, crispy or to your liking. Set aside for topping.
When pressure is released open the lid. Use an immersion blender to puree the soup to preferred texture (we did a full puree but some like it chunkier).
Stir in the yogurt, cream, pepper, and both cheeses (reserving some cheddar for topping).
Serve in bowls, top with green onion (or chives if you prefer), excess cheddar, and bacon bits.