Prepare the Herbs: Cut the lemongrass into 2" pieces and bruise them by smacking with the back of a chef's knife. Slice the galangal into thin rounds. Devein the makrut lime leaves and tear the leaves in half. Peel the shallots, and if they are large, cut them in half. Cut the stems off the Thai chilis.
Infuse the Broth: Add the water and chicken broth to a medium-sized pot over medium heat. Add the prepared herbs (except the Thai chilis). Allow the herbs to simmer for 10-20 minutes until the aroma is strong. At this point, you can strain them out for ease of eating, or leave them in if you prefer a stronger flavor.
Add the Chicken and Mushrooms: While the herbs are cooking, wash and prepare the mushrooms. Depending on which mushrooms you use, they can be left whole (beech), cut in half (straw), or sliced (white button). Cut the chicken into bite-sized pieces. Add the chicken and mushrooms to the broth and allow to cook until both are cooked through and tender.
Add the Coconut Milk: Then add the coconut milk and stir until well mixed. You can turn the heat down to medium low at this point so that the coconut milk doesn't get too hot and separate.
Season the Soup: Then season the soup with fish sauce and freshly squeezed lime juice. Start with 1 Tablespoon of each and adjust as necessary based on your taste preferences. Then add in the Thai chilis. For more spice, bruise the chilis with the back of a chef's knife to release their flavor. For less spice, simply add and stir without much manipulation. If you like, you can add in Thai roasted chili paste, cilantro, or green onions (these are optional variations).
Serve the Soup: Serve the finished Tom Kha Gai soup with jasmine rice as a stand alone meal, or on its own as part of a larger Thai meal. Enjoy!
Notes
Leftovers can be saved in the refrigerator and heated up in the microwave. The flavor of the herbs will become stronger the longer they are left in the soup, and, in my experience, the soup becomes even more delicious the day after it's made!