Place your dried shrimp in a small food processor and blend until they are broken down into a fine powder.
Make your paste by using a mortar and pestle to pound everything together. I generally start with the white peppercorns, garlic, shallots, and Thai chilis. Once this has formed a paste, I add the dried shrimp powder, krachai, gapi, and cooked shrimp.
Bring a pot of water to a slow boil. Add the paste you just made and allow it to cook for a few minutes.
Next add your vegetables to the soup, starting with the ones that require the longest cooking time. Once they are almost done, add the fresh shrimp and cook until they are done.
Add fish sauce to taste.
Take the soup off the heat. Add the lemon basil leaves and serve with fresh jasmine rice.
Notes
Recipe adapted from FoodTravel.tv recipes here and here.