Take the beef out of the fridge 30 minutes before cooking to bring it to room temperature. Dry it thoroughly and season with salt and pepper.
Heat 1 tablespoon of vegetable oil in a large Dutch oven over medium-high heat. Sear half of the beef pieces for about 1 minute on one side, then flip and continue to cook for 1-2 minutes until they develop a deep brown color. Remove the seared beef and set aside.
Add another ½ tablespoon of oil to the pan and repeat the process with the remaining beef tips.
After searing the second batch, lower the heat to medium and add butter. Once the butter starts foaming, add onions and bell pepper, seasoning them with salt and pepper. Cook until they are nearly tender, which takes about 4 minutes. Add garlic and thyme, cooking for an additional minute.
Sprinkle flour over the vegetables and stir with a wooden spoon to ensure it's fully mixed and coats the vegetables.
Gradually pour in the beef broth, about a half cup at a time, while scraping the bottom of the pan to loosen any browned bits. Stir constantly for a smooth gravy, avoiding adding all the broth at once.
Increase the heat to medium-high and bring the mixture to a boil. Return the beef tips and their juices to the pan, add Worcestershire sauce, then reduce the heat to a simmer. Let it cook for about 20 minutes until the beef finishes cooking and the gravy thickens.
Stir in parsley and serve the beef tips and gravy over cooked rice.