Place the chicken, quartered onions, 1 cup of chicken broth, beer, Delicioso Adobo, Worcestershire sauce, 1/2 of the cilantro, and garlic in a large pot or skillet over high heat. Bring to a boil, reduce the heat to medium-low, cover, and simmer until the chicken is cooked through, 30 to 35 minutes. Remove the chicken to a plate and set aside to cool; once cool shred and set aside. Strain the broth into a bowl through a fine-mesh sieve discarding the onion pieces.
Pour the broth into a measuring cup and add water to make 4 cups of liquid. Return it to the pot or skillet and add the rice, peas, carrots, green beans, ketchup, and salt. Stir well and bring to a boil. Let the liquid evaporate to just below the level of the rice, about 10 minutes, and then reduce the heat to low, cover, and cook until the rice is tender and fully cooked, 25 minutes.
Meanwhile, melt the butter in a large skillet over medium heat. Add the peppers and the remaining sliced onions and cook until they're tender, 8 minutes. Shred the cooked chicken meat discarding the skin and bones, and add the chicken to the vegetables. Cook until it is heated through, 2 to 3 minutes. Fluff the rice with a fork and add the chicken and vegetables to the rice mixture. Stir in the olives, sprinkle with the remaining cilantro and serve.
Combine all measured ingredients in a small glass jar with an airtight lid and shake to blend. Store in a cool, dry place for up to 2 weeks.
Note: This recipe for adobo is a staple seasoning for many of my Latin recipes. You can make a large batch, store it in an airtight container and use it as a flavor enhancer in your favorite dishes. *Achiote is also known as Annatto seeds