In a large pot, combine the steak, 1 chopped green bell pepper, 1/2 chopped onion, garlic cloves, peppercorns, bay leaves and enough water to cover the steak with about 2-inches of water. Set over medium-high heat and bring to a boil. Cook until the beef is fully cooked through and a fork goes through somewhat easily, about 15 to 20 minutes. Remove the steak from the poaching liquid and set on a plate. Discard poaching liquid, and let beef cool completely.
Once cooled, cut the steak into large cubes and place in a food processor. Pulse until the steak is finely chopped, about the size of Panko bread crumbs. Transfer to a large mixing bowl. Place the remaining chopped bell pepper in the food processor and pulse until finely chopped, about the same size of the beef. Transfer to the bowl of the beef. Add the remaining half of onion to the food processor and pulse until finely chopped as well. Add to the beef and bell pepper mixture, along with the juice of two limes, salt and pepper. Give it a big stir until it's all evenly combined. Taste the mixture and adjust seasonings accordingly, adding more lime juice, salt or pepper as needed. Cover with plastic wrap and chill for at least 1 hour before serving.
The salpicon is meant to be eaten cold with warm cooked rice, but if you prefer, you can serve it at room temperature as well. Enjoy!