In a bowl, add softened butter and work it with a spatula. Mix in powdered and vanilla sugar until creamy.
Then, add flour and ground walnuts, combining all ingredients into a dough first with a spatula, then with your hands. The mixture will feel and look crumbly at first, but that's totally fine.
Shape the dough into a ball, divide it into 2 logs, wrap it with plastic foil, and refrigerate minimally 2 hours or overnight.
Preheat the oven to 180°C (356°F) and line two baking trays with parchment paper.
Take a piece of the dough (each ball should be about 11 g), roll it into a ball, and then into a sausage. Do this quickly so the cookie dough doesn't soften too much. Shape each one into a crescent and place on the baking tray.
Bake one tray at a time for about 10 minutes. The vanilla crescent cookies shouldn't brown during baking, only get slightly golden on the edges.
After baking, let them cool down for 2-3 minutes on a baking tray, then transfer to a cooling rack.
Dust generously with powdered sugar or roll each cookie in powdered sugar, whatever option you prefer.