Turn on the Instant Pot to the Sauté function. Add the butter and olive oil. Once melted, add the cubed chicken and cook until it is no longer pink on the outside.
Add the diced onions and cook for 2 minutes. Stir in the minced garlic, oregano, salt, and black pepper, sautéing for another 30 seconds until fragrant. Add the cubed potatoes and carrots, stirring to combine.
Sprinkle flour on top and cook for another minute.
Cancel the Sauté function. Pour in the chicken stock and give everything a good stir, scraping up any browned bits from the bottom of the pot. Secure the lid, set the valve to "Sealing," and pressure cook on High for 3 minutes.
Once the cooking time is up, carefully perform a manual pressure release in short bursts to prevent any liquid from splattering out of the valve.
Remove the lid. Use a potato masher or an immersion blender to mash a portion of the potatoes directly in the pot until the soup reaches your desired thickness (leave it chunkier or make it smoother depending on preference).
In a medium bowl, whisk together the sour cream, and milk until completely smooth. Pour this mixture into the Instant Pot and stir it for about 30 seconds so the overall temperature stabilizes.
Then, add your freshly grated cheese one handful at a time, stirring constantly until the first batch melts before adding the next.
Ladle into bowls and serve warm, garnished with crumbled bacon, green onions, and a dollop of sour cream if desired.