Slice beef into 3/4-inch strips; then slice these pieces, at an angle, into smaller “tips.” Season beef with salt and pepper.
Heat oil in a large skillet over high heat until shimmering. Transfer in beef, arranging in a single layer. Let the meat sear until browned, 3 to 5 minutes, before turning over and browning the other side.
Reduce heat to medium and add tomato paste, garlic, and butter. Stir everything until the butter melts, and then stir in the flour. Cook and stir for 1 minute.
Stir in broth. Raise heat to high and bring to a simmer. Reduce to low, cover, and cook until beef is starting to get tender, about 1 hour and 15 minutes.
Meanwhile, preheat the oven to 425 degrees.
Uncover, turn heat to medium, and simmer, stirring occasionally, until the sauce has thickened, and the meat is tender, about 30 minutes.
While meat simmers, bake potato nuggets in the preheated oven until crispy and heated through, 20 to 25 minutes.
Taste beef tips and adjust the seasoning. Serve immediately over hot potato nuggets