In a large pot, place the chicken pieces, along with the onion, garlic, bay leaves, and 2 teaspoons of the salt, and cover with water. Set over high heat. Once it comes to a boil, reduce to medium heat, add the cubed potatoes and simmer for 20 minutes, until the chicken is just cooked through and the potatoes are soft. Transfer the chicken into a strainer and let cool. Then, transfer the cubed potatoes into another strainer and let cool.

For the sauce, in a medium saucepan, add the tomatoes and cover with water. Set over medium-high heat and simmer for 8 to 10 minutes until completely cooked and soft. Transfer the tomatoes to the jar of a blender along with the oregano, pickled jalapeño brine, and the remaining teaspoon of salt and puree until smooth.

Rinse and wipe dry the same saucepan used for the tomatoes and set over medium-high heat. Add 1 tablespoon of the oil, once hot, add the pureed tomato sauce and simmer for 5 to 6 minutes until darkened in color and thickened in consistency. Scrape onto a bowl.

In a large non-stick saute pan set over medium-high heat, add 2 tablespoons of the oil. Once hot, dunk the potatoes into the tomato sauce, then place in the saute pan and fry for 3 to 4 minutes per side, or until crisped and browned. Scrape onto a large platter and set aside.

Add the remaining 2 tablespoons of oil to the saute pan, and one by one, dunk the chicken pieces into the tomato sauce, then add to the saute pan. Fry for 3 to 4 minutes per side, flipping as need be, until completely crisped and browned. Place on the same platter as the potatoes.

Reduce heat to medium, pour in the remaining tomato sauce and simmer for 1 to 2 minutes, stirring constantly, while it bubbles and thickens. Pour the thickened tomato sauce over the chicken and toss to coat. Serve the chicken with a lot of sauce, the cooked potatoes or white rice.