Season beef with salt and pepper. Heat oil in a Dutch oven or heavy, lidded pot over medium-high flame. Working in batches, brown the beef. You don’t need to char it, just cook it on all sides briefly, a few minutes per batch. Using a slotted spoon, transfer to a bowl.
Reduce heat to medium and add the chouriço to the pot. Cook, stirring frequently, for about 3 minutes. Transfer to bowl with the meat with a slotted spoon.
Add onion and bell peppers to pot, stirring to combine and coat everything with oil. Cook for about 3 minutes, stirring frequently. Now is an optional but recommended step: transfer a generous cup of the bell peppers to a bowl (see Kitchen Notes). You’ll get some onion too, but try to mainly get bell pepper. Set aside.
Add garlic to pot with remaining pepper and onion mix. Sprinkle on paprika and stir to combine. Cook for an additional 2 minutes, stirring frequently.
Return beef and chouriço to pot, along with any accumulated juices. Stir to combine, then add wine, water and bay leaves. Stir together and raise heat to bring to a boil. Reduce heat to simmer, cover pot and cook for 1-1/2 hours, stirring occasionally. If the liquid is cooking away, stir in a little more water, as needed. We didn’t need water—add it cautiously so you don’t turn the stew into soup.
Meanwhile, prepare potatoes. Don’t peel them—just rinse under cold running water, then cut into large chunks. When the stew has cooked for 1-1/2 hours, add potatoes to the pot, along with reserved bell peppers. If necessary, add a little more water so they are just submerged. Cook for 30 to 45 minutes. Meat and potatoes should be completely tender.
Taste and adjust seasoning with salt, if needed. Remove bay leaves and ladle stew into individual bowls. Serve.