Cook the gnocchis in plenty of salted water according to the instructions, cook the broccoli for the last 7 minutes (or in an extra saucepan).
Fry the smoked bacon in a pan until crispy, add the milk, granulated broth and the processed cheese and bring to the boil briefly until a creamy sauce is formed. Season to taste with salt and pepper.
Drain the gnocchi and broccoli and mix with the sauce or serve separately.