Scrub the mussels under cold water. Discard any open mussels that do not close when tapped or tested with ice-cold water.
Fill a large saucepan with water and add roughly a handful of instant vegetable stock. Bring to a boil over high heat. Once boiling vigorously, add the mussels and reduce heat to simmer for 15 min.
Cut the onions into fine cubes. Press or finely dice the garlic. Chop the chives. Cut the chilli lengthways, quarter and remove the core. Roughly chop the Gorgonzola and sheep cheese.
In a small saucepan over medium heat, melt some butter. Add the onion, garlic, and chives and sweat for 3-4 min until softened. Deglaze the pan with a splash of white wine and reduce for 2 min. Stir in the chilli.
Add the cream and remaining white wine to the saucepan. Continue cooking over low heat, making sure the cream does not boil. Gradually add the chopped cheese while stirring constantly until melted and smooth. Season with salt and pepper to taste.
Drain the mussels after 15 min of cooking. Pour the sauce over the mussels and mix well.
Discard any mussels that remain closed after cooking.