Heat a Dutch oven or large pot over medium heat. Add the achiote and oil, then place the chicken pieces inside. Season with salt and black pepper, then immediately flip each piece and season the other side as well.
Leave the chicken to cook on that second side for about 10 minutes, until it starts to turn golden. Flip the pieces again and cook the other side for another 10 minutes, or until both sides are nicely browned. Remove from the pot and set aside.
In the same pot, add a little more oil and achiote if needed. Add the potatoes, carrots, onion, celery, and bell pepper all at the same time. Stir well and cook for about 5 minutes, or until the vegetables begin to soften and the potatoes start to turn slightly golden.
Add the garlic, oregano, cumin, salt, black pepper, and bay leaves. Mix well and cook for 1 more minute to release the flavors.
Pour in the chicken broth and bring it to a boil.
Return the chicken and any juices to the pot. Cover and cook for about 30 minutes over medium heat until the chicken is fully cooked and tender. When time has past, remove the lid and cook for 20-25 more minutes.
In a small bowl, mix the cornstarch with cold water until fully dissolved. Slowly pour it into the stew while stirring constantly. Cook for 5 more minutes, or until the sauce thickens slightly.