Combine the sliced chicken with the cornstarch, and 2 teaspoons each of neutral oil and fish sauce. Set aside.
To a medium soup pot over medium-high heat, add the remaining 1 tablespoon of oil and the mushrooms. Fry the mushrooms for about 5 minutes, or until tender. Add the chicken stock, lemongrass, galangal, lime leaves or zest, chilies and red curry paste (if using), and sugar. Bring to a boil over medium-high heat. Cover, lower the heat, and simmer for 6 minutes.
Stir in the coconut milk, and bring back up to a simmer over medium-high heat—watch the pot and don’t let it come up to a rolling boil, or the coconut milk could split. Add the chicken. Bring back up to a simmer, lower the heat to medium-low, cover, and cook for 8 minutes, until the chicken is cooked through.
Turn off the heat, and stir in the remaining fish sauce, lime juice, and fresh cilantro (or scallions/green onions, if you're not a cilantro fan). Season with salt to taste if needed. Ladle into bowls, and serve on its own or with some steamed jasmine rice!
Notes
Instruct your diners to discard any lemongrass, lime leaves, and galangal pieces—or pick them out before serving—as these are just meant to infuse the broth.