In a medium pot, combine 3 cups chicken stock with the ginger slices, torn kaffir lime leaves, bruised lemongrass stalks, and sliced chile pepper.
Bring the mixture to a simmer, then cover and reduce heat to low; simmer for 10 minutes to infuse the broth.
Remove from heat and strain the broth through a sieve, discarding the solids; if you want more heat, reserve the chile slices in the strained broth and discard them just before serving.
Return the strained broth to the pot and add the chicken pieces, cherry tomatoes, and mushrooms; bring to a simmer over medium heat.
Simmer for about 5 minutes, or until the chicken is cooked through and firm to the touch.
Stir in 3 tablespoons fish sauce, 2 tablespoons lime juice, and chopped fresh cilantro leaves to taste; adjust seasoning if desired, then serve hot.