Defrost the puff pastry. In the meantime, wash, peel and cut the potatoes into pieces. Put vegetable stock and potatoes into a pot and cook covered for about 15 minutes.
Roll out the puff pastry thinly on a floured work surface, brush with a little water. Sprinkle one half of the sheet with cheese, fold the other half of the pastry sheet over it, press it down slightly.
Cut into strips about 5 mm wide, turning each strip against each other to form spirals. Place cheese sticks on a baking tray lined with baking paper. Bake in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for approx. 10 minutes.
In the meantime, clean, wash and slice the leek. Cut the ham into strips and then into pieces about 2 cm long. Finely mash the potatoes with a hand blender, simmer the leek in it for about 6 minutes.
Let the ham stand for a short time, stir in the crème fraîche. Garnish the soup with oregano twigs and serve with the cheese sticks.