Dab tofu with a clean dish towel to remove excess moisture.
Heat 2 tablespoons peanut oil in a saucepan over medium-high heat. Fry tofu, turning occasionally, until golden brown, 5 to 8 minutes.
Trim ends of lemongrass stalks and peel off tough outer layers. Pound inner stalks gently with a heavy object to bruise and flatten out.
Heat remaining 1 tablespoon peanut oil in a saucepan over medium heat. Cook and stir curry paste until fragrant, about 1 minute. Stir in lemongrass, 1/4 cup coconut milk, eggplants, zucchini, carrot, green bell pepper, galangal, and lime leaves. Simmer until flavors combine, about 5 minutes.
Pour remaining coconut milk into the saucepan. Add soy sauce. Bring to a boil; reduce heat and simmer until carrot and green bell pepper are nearly tender, 10 to 15 minutes. Stir in fried tofu, bamboo shoots, and green peas. Simmer until bamboo shoots and green peas are heated through, about 5 minutes.