Set a 6-qt instant pot to LOW SAUTE function. Melt the butter then add sliced onions and slowly cook over medium heat, stirring occasionally until onions are a deep golden caramelized brown (about 20 minutes of cooking) Remove onions from instant pot, turn off instant pot, and set aside.
In a large bowl, combine ground beef, breadcrumbs, egg, garlic, salt, and pepper until combined. Form meatballs into 1-in balls.
Heat instant pot on HIGH SAUTE function and add oil. Brown meatballs in oil until golden.
Turn off SAUTE function and drain oil from instant pot. Arrange caramelized onions around meatballs and pour beer and beef broth over top. Top with thyme. Lock lid in place and cook meatballs on high pressure 8 minutes. Let release pressure naturally for 5 minutes.
Remove lid from instant pot and remove meatballs from instant pot. Stir flour-water into beef broth mixture until thickened. Transfer meatballs back to instant pot and top with shredded swiss cheese. Place lid back on instant pot and let stand 5 minutes until cheese is melted. Serve meatballs hot with pasta and enjoy!