Melt the fat in a pot. Stir in flour and sweat briefly. Add vegetable stock and milk while stirring. Bring to the boil, boil for 1-2 minutes and season with salt and pepper.
Cut the ham into strips. Add ham and gnocchi to the sauce and stir in. Pour into 4 greased casseroles (each with a capacity of approx. 400 ml) and sprinkle with cheese. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for about 15 minutes.
Wash the chives, shake dry and cut into small rolls. Sprinkle finished gnocchi with chives.