In a 6-quart Dutch oven or large stock pot, combine the chicken stock, 1/4 cup chopped cilantro, lime juice, kosher salt, lemongrass paste, ginger paste, and the chopped serrano chili. Stir to combine.
Bring the mixture to a boil over medium-high heat, then reduce to a simmer and cook gently for 15 minutes to allow the flavors to meld.
Add the sliced mushrooms and shredded chicken to the pot, stir to combine, and simmer for 5 minutes, until the chicken is heated through and the mushrooms are tender.
Remove the pot from the heat and stir in the coconut milk and brown sugar until smooth and fully combined.
Return the pot to low heat briefly to warm (do not boil), then ladle the soup into bowls and top with halved cherry tomatoes, additional cilantro, and hot sauce if desired.
