Start by prepping your ingredients. Peel and devein the shrimp, reserving the heads and shells for the broth. Remove the tough outer layers of the lemongrass, trim off the tops, and smash the bottom halves with the back of a knife, then cut into 2-inch pieces. Thinly slice the galangal, peel and halve the shallot, and gently tear the kaffir lime leaves to release their aroma.

In a medium pot over medium heat, add the shrimp heads and shells, smashed lemongrass, galangal, shallot, and kaffir lime leaves. Sauté for 2-3 minutes, stirring occasionally, until fragrant and lightly browned to draw out more flavor.

Pour in the chicken broth and bring to a boil, then lower to a simmer and cook for 15 minutes to infuse the flavors. Skim off any scum or foam that rises to the surface. Strain and discard the solids (keeping a few pieces of lemongrass or lime leaves) and return the clear broth to the pot.

Bring the broth back to a gentle simmer. Add the mushrooms and cook for 2-3 minutes. Stir in the tomatoes, Thai chili paste, fish sauce, and chopped Thai chili peppers and simmer for 1 minute. Add the shrimp and cook for 1-2 minutes, just until pink and cooked through.

Turn off the heat and stir in the lime juice and salt. Taste and adjust with more lime juice or salt as needed. Finish with chopped cilantro and serve immediately.