Pour 2 cups of the coconut milk and the chicken stock into a stockpot.
Cut the lower third off the stalks of lemongrass and discard the top portions. Trim the bottom of the stalk and cut each piece in half. Slice the peeled ginger into 4 pieces.
Add the lemongrass and the ginger to the stockpot then bring to a boil over medium heat. Once the coconut milk and stock have come to a boil, reduce the heat to the medium-low and simmer for 15 minutes.
Slice the chicken breast into very thin strips and add to the soup. Continue simmering for an additional 5 minutes or until the chicken has cooked through.
Remove the stalks of lemongrass and the ginger from the soup and discard. Stir in the fish sauce, the lime zest and lime juice along with the red pepper flakes, kosher salt and sugar.
In a small bowl, whisk together the remaining ½ cup coconut milk with the cornstarch. Stir into the soup and cook for about 15 minutes until the soup is warmed through and slightly thickened.
Serve with a sprinkling of toasted coconut and chopped cilantro.
To toast coconut, spread sweetened coconut flakes onto a rimmed baking sheet. Bake at 350-degrees for about 7 to 8 minutes or until golden. Stir frequently to keep the coconut from burning.