Bring the broth, ginger, garlic, fish sauce, cilantro stems, sugar, half of the sliced chiles, and one-quarter of the chopped tomatoes to a boil in a large saucepan over medium-high heat. Reduce the heat to low and simmer for 20 minutes. Strain the broth through a fine-mesh strainer into a large bowl, pushing on the solids to extract as much liquid as possible.
Return the broth to the pan and bring it to a simmer over medium-high heat. Add the mushrooms and the remaining chiles and cook for 2 minutes. Add the shrimp and cook for 1 minute longer. Remove the soup from the heat and add the lime juice. Evenly portion the remaining chopped tomato and the chopped cilantro among individual bowls and ladle the soup over top. Serve immediately.