"My Khmer sons both love this soup at our favorite Cambodian restaurant, Chez Sovan, in San Jose, CA.
This is my attempt to match the flavors at home.
My oldest son's comment on trying the soup was, Mmm so close, make some more! Serve with warm baguette."
Combine chicken broth, lemon juice, lemon zest, garlic, lime juice, lime zest, peppercorns, soy sauce, ginger, fish sauce, and chile pepper in a large pot.
Remove tough outer stalks from lemongrass. Halve inner stalks and cut into 3-inch peaches. Place in a resealable plastic bag and pound with a hammer until bruised.
Fill bag with water and pour into the pot. Bring soup to a boil; reduce heat and simmer until flavors combine, about 20 minutes. Strain with a small mesh strainer, discarding solids. Pour strained liquid back into the pot.
Stir chicken, green onions, carrot, cabbage, mung bean sprouts, Chinese mushrooms, cilantro, Thai basil, and mint into the soup. Simmer over medium heat until carrot is tender, about 10 minutes.
Spoon 1 teaspoon garlic chile paste into the bottom of each serving bowl and ladle soup on top.