Sauté Aromatics: Heat the peanut oil in a deep pot with a lid over medium heat. Add the minced garlic and sliced lemongrass and stir until fragrant.
Build the Tomato Base: Add the tomatoes and 2 tablespoons of water to the pot. Simmer for about 2 minutes until the vegetables begin to break down.
Season: Stir in half of the fish sauce and half of the sugar.
Simmer the Eggplant: Add the eggplant pieces to the pot along with 1 cup of water. Stir in the remaining fish sauce, the remaining sugar, red chili strips, turmeric, and pepper.
Cook: Cover and simmer until the eggplant is soft and velvety, about 5 to 10 minutes. (Note: For a smoother stew, you can pulse the mixture in a blender and return it to the pot).
Finish: Garnish with fresh chopped basil and diagonally sliced green onions before serving.