Place the tofu between two plates and top with a heavy object. Allow this to rest for 5 minutes in order to remove excess liquid. Heat a pan with a teaspoon of oil over medium-high heat. Add the tofu and cook until all sides have slightly browned. Transfer to a plate.
Add another 2 tsp of oil in the pan along with all of the vegetables. Cook until the vegetables have softened lightly, about 8 minutes. Add the tofu and mix together.
Add the green curry paste, coconut milk, and vegetable broth. Bring to a boil. Reduce the heat and simmer for 10 minutes. Add the fish sauce. Serve with a bowl of rice or rice noodles and lime quarters.