Place the cubed chicken breasts into the basin of a 4-quart or larger slow cooker.

In a medium bowl, whisk together the full-fat coconut milk, chicken broth, red curry paste, brown sugar, fish sauce, minced ginger, and minced garlic until the curry paste is fully dissolved and the mixture is uniform.

Pour the coconut curry sauce mixture evenly over the chicken in the slow cooker, ensuring all pieces are submerged as much as possible.

Cover the slow cooker. Cook on LOW for 6 to 8 hours, or on HIGH for 3 to 4 hours, until the chicken is tender and easily shredded with a fork.

Once cooked, use two forks to lightly shred the chicken directly in the sauce, or leave them as chunks depending on preference.

Taste the sauce and adjust seasoning if necessary (add more fish sauce for saltiness or curry paste for heat). Serve hot over steamed jasmine rice, garnished with fresh cilantro and a squeeze of fresh lime juice.