Melt butter in a large saucepan over medium-low heat; add the chopped vegetables and prosciutto and cook until softened, about 5 minutes.
Increase the heat and add beef mince; cook, stirring often, until well browned.
Pour in wine and simmer until the alcohol evaporates. Add passata and season to taste with salt and pepper. Reduce heat and cook for 1 hour, stirring from time to time.
Preheat oven 200 C / Gas 6.
Cook the potato gnocchi in plenty of salted water. When they start to float to the top, they are cooked, about 2 or 3 minutes. Drain and transfer into a bowl. Fold in 20g butter, bolognese sauce and 3/4 of the grated Parmesan.
Transfer into a large baking dish and top with remaining cheese.
Bake in preheated oven for 15 minutes, grilling for the last 2 or 3 minutes to brown the top if necessary.