Cut steak into 4 rectangular pieces. Pat dry with paper towels; season all over with 1 1/2 teaspoons salt.

In a large pot over medium-high heat, heat 2 tablespoons oil. Working in batches, cook steak until browned on both sides, 5 to 6 minutes. Transfer to a plate.

In same pot over medium heat, heat remaining 2 tablespoons oil. Cook bell peppers, onion, and 1 1/2 teaspoons salt, stirring occasionally, until slightly softened, 4 to 5 minutes. Add garlic, tomato paste, paprika, cumin, and oregano and cook, stirring occasionally, until vegetables are softened and spices are aromatic, 1 to 2 minutes more.

Add wine, scraping any browned bits from bottom of pan, and cook, stirring occasionally, until reduced by half, about 2 minutes. Add tomatoes with their juices and bay leaves. Mash down on tomatoes to break up, then nestle beef into stew. Add water to cover beef, if needed, and bring to a simmer. Reduce heat to medium-low; cover and simmer until steaks are tender enough to shred, 2 1/2 to 3 hours. Transfer steaks to a plate and finely shred with 2 forks.

Stir shredded steak back into stew. Bring to a simmer and cook, stirring, until liquid has reduced to a sauce that coats steak, 5 to 10 minutes. Stir in olives; season with salt.

Spoon ropa vieja over rice and beans. Top with cilantro.