Heat 2 tablespoons of vegetable oil in a large saucepan. Fry 4 tablespoons of Thai green curry paste, 2 minced garlic cloves, 2 teaspoons of grated ginger, and 1 tablespoon of lemongrass paste until mostly dry, 2-3 minutes.
Stir in 1 cup of chicken broth, 400ml of full-fat coconut milk, 1 teaspoon of fish sauce, 1 teaspoon of sugar, and 6 makrut lime leaves. Bring to a simmer.
Add 350g of boneless chicken thighs, sliced, and cook at a gentle bubble for 7 minutes.
Add 2 small Japanese eggplants, cut into chunks, and cook for 5 minutes, until soft.
Add 1½ cups of snow peas and 16 Thai basil leaves and cook briefly, until the peas are tender-crisp. Adjust with more fish sauce or sugar to taste.