Add 1 cup white onion slices, 1 tablespoon chopped fresh garlic, ½ red jalapeño pepper, 3 slices fresh galangal , 1 stalk lemongrass, 10 lime leaves, 1 tablespoon red Thai curry paste, and 4 cups chicken broth. Stir until all ingredients are incorporated.
Place lid on slow cooker. Cook mixture on HIGH 3 hours, or LOW 6 hours. Stir mixture occasionally.
When cook time ends, use slotted spoon to remove solids from slow cooker, leaving liquid behind.
Add 2 13.5-ounce cans full-fat coconut milk (at room temperature), 1 pound chicken breasts, and 8 ounces white mushroom caps to slow cooker. Stir to incorporate.
Place lid on slow cooker. Cook ingredients on HIGH 1 hour or LOW 2 hours, until chicken breast pieces are fully cooked.
Once chicken is cooked through, add 2 tablespoons brown sugar, 2 tablespoons fish sauce, and 2 tablespoons fresh lime juice. Stir to incorporate, then taste mixture and adjust brown sugar, fish sauce, and lime juice as desired.
When satisfied with flavor of soup, ladle soup into serving bowls. Garnish each bowl with thinly sliced green onions and chopped fresh cilantro. Serve immediately.