First prepare the gnocchi in salted water according to package directions. Meanwhile, cut the ham into cubes of any size.
Drain the gnocchi and leave them in the colander. It is best to cover them so they stay warm.
Return the pot to the stove and reduce the heat so nothing burns. Add the cream and processed cheese to the pot and melt the cheese over medium heat, stirring constantly.
When the cheese has melted completely, add the cooked ham and heat through. Remove the pot from the heat and add the gnocchi. Let everything simmer for about half an hour without heat.