Heat the oil in a large stock pot over medium high heat.
Season the meat generously with salt and pepper. Add the meat to the oil and cook until browned, about 5-7 minutes. You may need to brown the beef in batches to get a good sear. If so, drain any accumulated grease between batches.
Add the seared meat to the slow cooker.
Add the onion, bell pepper, mushrooms and garlic.
Whisk together the the broth and brown gravy mix. Pour the broth over the top.
Add the pepperoncini peppers and butter to the top.
Cook on low for five hours or on high for three hours.
Remove the lid and spoon out a few tablespoons of the cooking liquid into a small mixing bowl. Whisk in the cornstarch until smooth. Stir the cornstarch slurry into the beef tips.
Replace the lid and continue to cook for one more hour.
Remove the pepperoncini peppers before serving. Discard the peppers or remove the stems, chop them up and add them back into the pot.
Season the beef tips with salt and pepper to taste. Serve over hot egg noodles, rice or mashed potatoes.