Place chicken breasts in a slow cooker. Add the onion, thyme leaves, garlic powder, allspice, smoked paprika, salt, pepper, jerk seasoning paste, chicken broth, browning sauce, and lime zest + juice.
Massage the ingredients into the chicken (wear gloves if preferred) until everything is evenly coated.
Cover and cook on low for 6 hours or high for 4 hours, until the chicken is cooked through and fall-apart tender.
While the chicken cooks, prepare the mango salsa. In a medium bowl, combine diced mango, bell pepper, red onion, cilantro, lime zest + juice, and a pinch of salt.
Toss well and refrigerate, covered, to let the flavors meld together.
Once the chicken is done, shred it directly in the slow cooker using two forks. Stir the shredded chicken into the cooking juices for extra flavor.
Serve the shredded jerk chicken in warm tortillas. Top with fresh mango salsa, chopped cilantro, and a squeeze of lime juice.