Heat 3 tablespoons of oil in a wok. Add the green curry paste and sauté for a few minutes. Deglaze with 5 cl of coconut milk.
Add the rest of the coconut milk and the vegetable stock. Bring to the boil, then lower the temperature. Add the whole kaffior leaves. Add the lemongrass sticks cut into pieces of about 5 cm.
Season with fish sauce, salt and pepper. For a vegetarian version, replace the fish sauce with a little more salt. Cook over a low heat for 10 minutes.
Add then, the broccoli, courgettes, snow peas and mushrooms. Cook over low heat for 5 minutes.
Check the taste and readjust if necessary. Add lime if the curry is too sweet. Add salt or fish sauce if it lacks salt.
Just before serving, remove the Thai basil leaves from their branches and add them to the curry.
Serve with Thai rice.