Heat oil in a pot over medium heat. Add garlic and ginger, and sauté until fragrant (about 1 minute).
Stir in the green curry paste and cook for another minute to release the flavors.
Pour in the coconut milk and vegetable broth, stirring until combined.
Add soy sauce and sugar, and bring the mixture to a gentle simmer.
Toss in the tofu and eggplant, letting them soak up the curry goodness for 5 minutes.
Add bell peppers, zucchini, and broccoli, and cook for another 5 minutes until tender but still vibrant.
Taste and adjust seasonings if needed. More soy sauce for saltiness, more sugar for sweetness, or more chili for spice.
Turn off the heat, toss in fresh basil, and stir gently.
Serve hot over jasmine rice, and squeeze a lime wedge over the top for extra brightness.