Heat the olive oil in a medium pot over low heat. Add the onion and cook gently until softened, about 4 to 5 minutes.
Increase the heat to medium-high and add the curry paste. Fry until it just starts to catch on the bottom of the pan, about 1 minute.
Add the white wine and deglaze the pan, scraping up any paste. Add the cleaned mussels immediately and put the lid on. Steam for 2 to 3 minutes until the shells have opened. Discard any that remain closed.
Add the coconut milk or cream, stir to combine, and cover for a further minute to heat through.
Scatter over the coriander or parsley and serve immediately with crusty bread.