Set Instant Pot to "Sauté" and add the ground beef. Cook, stirring often, until beef is crumbled and no longer pink, approximately 5 minutes. Transfer beef to a paper towel-lined plate and carefully drain the fat.
Heat butter and oil and add the diced onion to the pot. Sauté, stirring occasionally, until onion is translucent (about 3 minutes). Add minced garlic, chili powder, cumin, black pepper and salt.
Add the chicken stock and water, while scraping the brown bits off the bottom of the pot insert, to deglaze the pan. Turn Instant pot off.
Add the diced tomatoes with green chilies, diced tomatoes, black beans, kidney beans, pasta and browned beef. Stir, being sure the liquid covers pasta.
Lock the lid in place and close the release valve.
Set Instant Pot to Manual/Pressure Cook on HIGH and set timer to 4 minutes.
When the cook time ends, turn off the pressure cooker, and use a quick pressure release. (To reduce splattering, cover the release valve with a lightweight kitchen cloth.)
When the red valve drops, carefully remove the lid. Stir the mixture.
Set the pot to "Sauté" and add the milk and 1 cup of cheese. Stir until the cheese melts. Repeat this process until all the cheese has been added. Stir until pasta is tender, approximately 2 more minutes. Add the parsley and stir.
Season to taste with kosher salt and black pepper.