Peel and devein the shrimp, keeping the tails on if you like. Reserve the shells.
Make the shell broth (optional but recommended). Put the shrimp shells in a pot with the water, bring to a boil, then simmer 10 minutes. Strain and discard the shells. (If using chicken broth instead, skip to step 3.)
Return the broth to the pot. Add the lemongrass, galangal, kaffir lime leaves, and chiles. Bring to a boil, then simmer gently 8 minutes until fragrant. Think of this like making tea — a gentle infusion, not a hard boil.
Add the mushrooms and the roasted chili paste; stir to dissolve the paste. Simmer 2 minutes.
Add the shrimp and cook 3 minutes, just until pink, firm, and opaque. Do not overcook — shrimp go rubbery fast.
Take the pot off the heat. Stir in the fish sauce and lime juice; taste and adjust — the soup should read sour first, then salty, then hot. Add the cilantro and green onions.
Ladle into bowls, leaving the lemongrass stalks, galangal slices, and lime leaves behind in the pot or pushed to the side of the bowl. Serve with jasmine rice.