Boil pasta to al dente according to instructions. Drain and set aside.
(Optional) If you plan to cook the baked version, preheat oven to 220 degrees C (430 F).
Heat oil in a nonstick skillet over medium heat. Add green curry paste and stir until combined with the oil and oil is bubbling.
Add flour and cook, stirring until the flour is incorporated evenly and forms a paste, 2 to 3 minutes.
Slowly blend in coconut milk, whisking as you pour, so that the liquid fully incorporates with the curry paste and forms a thin paste. Add the rest of the coconut milk and the fish sauce. Stir and cook for 2 minutes, until the paste is evenly mixed and can coat a spoon. Add salt and mix well.
(Optional) Stop heat and add mozzarella cheese. Mix a few times until cheese is melted. (Skip this step or replace mozzarella with vegan cheese to cook a vegan dish.)
Add the cooked pasta to the skillet and mix well.