Heat oil in a skillet over medium heat. Place chicken chunks skin-side down and cook until golden and rendered, 15–20 minutes. Stir only 2–3 times.
Add tomatoes, bell peppers, onion, garlic, bay leaves, cumin, oregano, salt, and pepper. Cook 10–12 minutes until soft and jammy. Add more oil if needed.
Transfer mixture to a food processor and pulse until a thick, smooth paste forms. Let cool.
In a large bowl, combine masa harina with warm water gradually. Knead until dough is soft, pliable, and moist but not sticky. Adjust with water or masa as needed.
Mix cooled chicken chicharrón with refried beans, mozzarella, and Monterey Jack until well combined.
Scoop a golf ball–sized portion of dough. Flatten into a thick disc, add 2–3 tbsp filling, and fold edges to encase. Roll into a ball, then flatten into a 5-inch disc.
Lightly oil or wet hands as needed to prevent sticking.
Heat a comal or skillet over medium. Cook pupusas 3–5 minutes per side until golden with charred spots. Filling may bubble slightly.
Serve warm with curtido and salsa.