Sort through the beans and remove any foreign objects, like small stones.
Rinse the beans, add them to a large pot or bowl and cover with 3-4 cups of water; let the beans soak overnight. Drain and rinse the beans, they’re now ready to cook.
For a quicker soaking method, sort and rinse as above. Add the beans and 6 cups of water to a large pot. Bring the water to a boil; cook the beans for 2 minutes. Remove the pot from the heat, cover and set aside for one hour. Drain and rinse the beans, they’re now ready to cook. I use the quick soak method and it has worked well so far.
While the beans soak prepare the sofrito: Heat the olive oil in a skillet over medium heat. Add the onions and cook for 5 minutes, stirring frequently. Add the tomato paste, garlic, salt, oregano, cumin and black pepper, stir well to combine. Cook 1 minute, stirring constantly. Remove the skillet from the heat.
Add the beans, 10 cups of water, the smoked meat, the prepared sofrito and the chicken base (if using) to a large pot, stir well to combine. Bring the water to a boil, reduce the heat to medium-low, cover and simmer for 1 hour, stirring occasionally.
Uncover the beans, remove the smoked ham and let cool. Cover the beans and continue cooking. When the smoked pork is cool enough to handle, remove the meat from the bone. Discard the bones, and any fatty pieces. Chop the meat into bite sized pieces and return it to the pot.
Continue to cook the beans for another 15-20 minutes. Taste the beans, if they're still firm, cover the pot and continue cooking for 30 minutes. Try them again.
When the beans are soft, uncover the pot to allow the liquid to thicken. This process could take anywhere from 15 to 45 minutes, depending on how much liquid is in the pot and how thick you want them. Keep the beans at a simmer, raise the heat a bit if necessary, stirring occasionally.
Taste the red beans; add salt and pepper to taste, if needed.