Preheat the oven to 375 degrees F. Pat the chicken dry and season with salt and pepper. Melt the butter with the oil in a large oven proof pan, with a lid over medium-high heat. Add the chicken, skin-side down, and cook until well browned, about 7 minutes.
Turn chicken and cook until other side browns lightly, about 2 minutes more. Transfer chicken to a plate and set aside.
Add the onion to the pan and cook, stirring often, until soft, 3 to 5 minutes. Add the garlic and cook 1 minute longer. Add the red pepper and cook, stirring, until softened, about 2 minutes.
Add the sazon goya, cumin, rice, and season with salt. Stir until the rice is coated. Add the broth, stir well and increase the heat to high and boil until liquid begins to be absorbed into the rice, about 2 minutes.
Add the chicken to the rice. Cover and transfer the pan to the oven and bake until the rice is soft and chicken is cooked, about 25 minutes.
Remove the cover, fluff the rice and stir in the peas, carrots and green beans. Move the chicken to the top to make the skin crispy. Cook for 10 minutes more. Cover and let sit, about 5 minutes. Season with salt and pepper, sprinkle fresh cilantro and serve.