Peel and crush (mince) the garlic, finely chop the parsley and basil and add to the garlic. Soften the butter (a few seconds in a microwave) and add this plus the cheese then grind or pound to a smooth paste.
Wash the mussels then place them in a large pan, pour over the wine and bring to the boil. Cover and cook until the shells have opened (about 7-8 minutes), discarding any that do not open. Set the mussels to one side and keep the liquor for the moment.
Remove the empty half shell from each mussel. Spread the remaining mussel in its shell with the herb butter and arrange them on individual ovenproof dishes. Moisten with a little of the retained liquor then brown under a preheated hot grill (broiler) for about 5 minutes until they are lightly browned.
Serve at once, garnished with a sprig of basil or parsley. (If you don't have individual ovenproof dishes, arrange the mussels on a large ovenproof plate and grill. Then split them onto individual plates but be careful because the shells and the butter will be very hot.)