In a pot, combine the 3 cups chicken stock, ginger slices, torn kaffir lime leaves, bruised lemongrass stalks, and sliced chile pepper; bring to a simmer.
Cover, reduce heat to low, and simmer for 10 minutes to infuse the broth; then strain the broth and discard the solids. (If you want extra heat, keep the chile slices in and remove them just before serving.)
Return the strained broth to the pot and bring to a medium simmer. Add the chicken pieces, cherry tomatoes (or tomato wedges), and mushrooms; simmer for 5 minutes until the chicken is cooked through.
Stir in the fish sauce, squeeze in the lime juice, and add fresh cilantro leaves; taste and adjust seasoning if needed, then serve immediately.