Marinate the chicken: In a bowl, combine soy sauce, vinegar, minced garlic, bay leaves, black pepper, and brown sugar. Add chicken thighs, cover, and marinate for 30 minutes (or overnight for deeper flavor).
Cook the chicken adobo: Transfer the chicken and marinade to a skillet over medium heat. Add 1/2 cup of water, bring to a simmer, cover, and cook for 25 minutes. Uncover and cook for an additional 10-15 minutes until the sauce thickens and the chicken is tender.
Shred the chicken: Remove the chicken from the skillet, discard the bay leaves, and shred the chicken using two forks. Return the shredded chicken to the sauce and coat thoroughly.
Prepare the tortillas: Warm tortillas in a dry skillet or microwave until pliable.
Assemble the tacos: Fill each tortilla with shredded chicken adobo. Top with shredded cabbage, chopped cilantro, avocado slices, and pickled red onions. Serve with lime wedges on the side.