Spread the tofu over a paper towel–lined baking sheet and let it drain for 20 minutes to remove excess moisture. Gently press the cubes dry with paper towels, then season with salt and pepper.

Heat one tablespoon of oil in a 12-inch nonstick skillet over medium-high heat until the oil is shimmering. Add the squash and cook until golden brown, 8 to 10 minutes, then transfer to a large bowl.

Add another tablespoon of oil to the empty skillet and return to medium-high heat until shimmering. Add the eggplant and cook until golden brown, 5 to 7 minutes, then transfer to the bowl with the squash.

Heat the remaining tablespoon of oil in the skillet over medium heat until shimmering. Add the onion and cook until softened and lightly browned, 5 to 7 minutes. Stir in the garlic, ginger, and lemongrass and cook until fragrant.

Stir in the coconut milk, broth, the browned vegetable mixture, and the tofu. Bring the liquid to a simmer, then reduce the heat to medium-low and cook until the vegetables are tender and the sauce has slightly thickened, 15 to 20 minutes.

Remove the skillet from the heat and discard the lemongrass stalk. Stir in the cilantro and lime juice, then season with soy sauce and pepper to taste. Serve hot, sprinkled with scallions.