Into a large deep skillet over medium heat, add 1 tablespoon vegan butter. When the butter is melted, add the beef tips. Cook 5 minutes, turning frequently until browned on all sides. Remove from the skillet and set aside. Do not wipe out the skillet.
Add the remaining 1 tablespoon of butter. When butter is melted, add the chopped onion. Cook 3 minutes, until softened. Stir in all-purpose flour and cook 2 minutes. Add garlic and continue cooking an additional 1 minute.
Whisk in the beef-style broth, Worcestershire sauce, and tamari sauce.
Add beef tips back into the skillet. Stir to coat with the sauce.
Bring to a boil then reduce to a simmer. Cover the skillet, leaving a little space for steam to escape, and simmer 30 minutes. Stir every 5 minutes.