Start by preparing the beef. If you are using a chuck roast, remove the silvery membrane and cut the meat into bite-sized pieces.
In a large bowl, mix together the flour, smoked paprika, salt, and pepper. Toss the beef pieces in this flour mixture until evenly coated.
In a heavy iron skillet or Dutch oven, melt the butter over medium heat. Add the sliced mushrooms and sauté until they turn golden brown.
Toss in the chopped onion and diced poblano pepper to the skillet, sautéing them for about 3 minutes until softened.
Remove the sautéed vegetables from the skillet and set them aside for now.
Add oil to the skillet and heat it until hot. Quickly sear the beef on all sides until beautifully golden brown. Remove it from the skillet and set aside.
Deglaze the skillet by adding the red wine and most of the beef stock (saving a bit for later). Bring this mixture to a gentle simmer, scraping up any browned bits from the bottom.
If you are using it, add the guijillo pepper and let it simmer for 5 minutes.
Return the beef and sautéed vegetables to the skillet. Cover it with a lid slightly ajar to allow steam to escape.
Let the beef tips and gravy simmer on low heat for 3 hours, stirring occasionally to prevent sticking. Add more beef stock if needed to keep it from drying out.
After 3 hours, your beef should be wonderfully tender and the gravy thickened to perfection. If it’s not thick enough, simmer it uncovered for a few minutes or use a cornstarch slurry to thicken it.
Serve your delightful beef tips and gravy over mashed potatoes, rice, noodles, or your favorite side dish.