Put the gnocchi in plenty of boiling salted water and let simmer for 2-3 minutes. Drain.
Clean, wash and halve the mushrooms if necessary. Drain the tomatoes and cut into small pieces.
Heat oil in a pan. Fry the ham in it, remove it. Fry the mushrooms vigorously in the frying fat. Fry the gncocchi and tomatoes briefly, season. Pour in the cream, bring to the boil and simmer for about 2 minutes. Wash the basil, pluck the leaves off. Season the gnocchi pan to taste. Scatter the basil and ham on top.