Make a spice paste by pounding the lemongrass, chilies, garlic, galangal and kaffir lime leaves together. You can make the spice paste as smooth or as coarse as you like.
Heat the cooking oil. Saute the spice paste over medium-low heat with a splash of fish sauce.
When the color of the paste deepens, add the sliced shallots. Continue sautéing for a minute.
Add the pork to the pan. Stir to coat the meat with the spice paste.
Pour in the broth. Season with more fish sauce. Bring to the boil.
Add the squash. Allow the liquid to boil. Lower the heat, cover and simmer for five minutes.
Throw in the eggplant wedges and the Thai basil leaves. Taste the broth and add more fish sauce, if needed.
Simmer for another seven to ten minutes until both the eggplants and squash are tender.
Sprinkle in the scallions.
Serve your gaeng om immediately.