Combine the cubed stew meat in a bowl with the flour. Toss to coat.
Set the Instant Pot to saute. Once hot, add the flour-coated meat along with the butter.
Brown the meat, turning only a handful of times until all of the pieces are just browned.
Add the broth and then scrape the bottom of the pot with a wooden spoon to deglaze - this helps make sure the pot can come to proper pressure.
Turn off the saute setting and then add the potatoes, carrots, Worcestershire sauce, tomato paste, minced onions, and garlic. Stir.
Put on the lid and set the valve to sealing. Cook on manual high for 40 minutes.
Once the cooking time is done - allow for a natural pressure release for 30 minutes, then do a quick release of any remaining pressure.
Carefully remove the lid, and then check the tenderness of the meat. It should be falling apart and the vegetables should be "fork-tender".
Stir the stew again before serving.