Activate the Instant Pot's 'Sauté' mode and wait for it to indicate 'Hot'. Add ground beef, breaking it apart as it browns, and cook for 6 to 8 minutes until fully done.
Stir in the Italian seasoning, garlic powder, dried minced onion, kosher salt, and black pepper. Sauté for another couple of minutes to infuse the meat with seasoning.
Turn off the 'Sauté' setting. Pour in the beef stock and stir, scraping the bottom to deglaze thoroughly.
Evenly scatter the farfalle pasta into the pot, gently press it into the liquid without mixing. Layer the vodka sauce over the top—do not stir.
Seal the lid, set the valve to 'Sealing', and choose the 'Manual' or 'Pressure Cook' setting. Cook on High Pressure for 5 minutes.
Let the pressure naturally release for 2 minutes, then manually release the rest. Once the pin drops, open the lid.
Immediately fold in mozzarella and Parmesan cheeses, stirring until both are melted and fully incorporated into the creamy sauce.