In a 6-quart Dutch oven or large stock pot, combine the chicken stock, chopped cilantro, lime juice, kosher salt, lemongrass paste, ginger paste, and chopped serrano chili. Stir to combine and bring to a boil over medium-high heat.
Reduce the heat to a simmer and cook for 15 minutes to allow the flavors to infuse.
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.
Stir in the coconut milk and brown sugar until smooth and fully combined; heat gently so the soup is warm but not boiling.
Adjust seasoning if needed, then ladle into bowls and top with halved cherry tomatoes, additional cilantro, and hot sauce if desired.