Cut chicken pieces to desired size. Pat dry and salt liberally.
In a large heavy bottom pot, add oil and heat on stove over high heat. If you plan to cook your guisado in the oven, preheat it to 325 degrees F and make sure to use an oven-safe pot and lid.
Once the oil is hot, add chicken pieces and sear until golden brown on all sides. Work in batches to avoid crowding the pan. Set chicken aside.
Turn heat down to medium. Add chopped onions and carrots, if using, to the remaining oil in the pot. Sautee, stirring occasionally and scraping up brown bits from the pot, until softened, about five minutes.
Add garlic and sautee until fragrant, about 2 minutes.
Add sofrito and spices. Cook for a few minutes, stirring often.
Add tomato paste and mix well, allow to cook a few minute while the paste caramelizes slightly.
Add alcaparrado mix or stuffed olives and capers and stir thoroughly.
Add reserved chicken back to the pot, making sure to return accumulated juices along with it.
Add enough chicken stock or water to almost cover the chicken, but do not fully submerge it. If using chicken stock cube, add it now.
Add chopped potatoes along with any other optional vegetables you are adding.
Add one teaspoon of salt.
Bring to a boil, then, either transfer to preheated oven with lid on, or reduce heat to low and bring to a simmer on the stove covered.
Cook for about 40 minutes. Check for doneness. If the chicken is fully cooked, taste and adjust salt level.
With lid removed, return pot to the oven OR continue simmering on stove, allowing sauce to thicken slightly. Cook until chicken is super tender and falling off the bones.
Garnish with chopped cilantro if desired, and serve with white rice and your favorite accompaniments.