For the vanilla crescents, first beat the butter, vanilla pulp, sugar, egg and lemon zest grated with a hand mixer until thick and creamy. Add the hazelnuts and sift the flour over them.
Work everything into a smooth dough, first with a wooden spoon, then by hand. Wrap in plastic wrap and refrigerate for 1 hour.
Preheat the oven to 180 °C.
Take walnut-sized pieces of the dough, form them into a roll and then into croissants.
Place on baking sheets lined with baking paper and bake for 15 minutes.
Place the vanilla crescents on a cooling rack and sprinkle with powdered sugar while still warm. Allow to cool.