Heat an electric skillet for 400 degrees F (200 degrees C) to 450 degrees F (230 degrees C); add vegetable oil. Cook beef tips in the hot oil until browned on all sides, about 5 minutes.

Heat olive oil and butter in a skillet over medium-high heat; saute onion and garlic until softened, 5 to 10 minutes. Add onion mixture, beef stock, 1 cup cooking wine, soy sauce, Worcestershire sauce, and browning sauce to beef tips.

Cover electric skillet, reduce temperature to 200 degrees F (95 degrees C) to 250 degrees F (120 degrees C), and simmer, stirring occasionally, until beef is tender, about 1 hour. Add 2 cups water as needed to maintain moisture in the skillet.

Pour remaining cooking wine into beef tips mixture. Stir cornstarch and 2 tablespoons water together in a bowl until smooth; stir into liquid mixture in the electric skillet and cook until thickened, about 5 minutes more.