Brown beef over high heat in a large saute pan and season with 1/2 teaspoon fine sea salt. Use a metal spoon to break it up into small pieces.
While meat is browning, dice onion, pepper, and tomato, and mince garlic. If olives are large, cut in half.
Once the beef is cooked, turn down the heat to medium and add olive oil. Add chopped veggies, along with Cuban seasoning, olives, or capers, plus 2 Tablespoons of the brine from the olives. Add tomato paste and water, and simmer for about 20 minutes. Taste and add more salt if necessary.
Traditionally picadillo is served with white rice.