Add the flour and softened butter to a mixing bowl and rub them together with your fingertips until you get a sandy, crumbly texture.
Stir in the sour cream and start bringing the dough together with your hands or a spatula.
Sprinkle in the vanilla sugar and a pinch of salt, then mix until evenly distributed in the dough.
Add about half a teaspoon of finely grated lemon zest, using a fine grater so it blends well into the dough.
Knead the dough by hand just until it comes together in a smooth ball; if the dough feels too soft or sticky, add an extra 1–2 tablespoons of flour (about 10–20 g)
Wrap the dough tightly in plastic wrap and refrigerate it for about 2 hours to firm up and relax the gluten.
Meanwhile, get your jam ready in a small bowl; here we use strawberry jam, but you can use any favorite flavor.
Finely chop or pulse the walnuts in a blender, then add them to the jam and mix until you have a thick, spoonable filling.
Once the dough has chilled, lightly flour your work surface, remove the dough from the plastic, and roll it out evenly with a rolling pin to a medium thickness.
Using a small round cookie cutter or a small drinking glass, cut out circles from the rolled dough.
Place a small teaspoon of the walnut and jam filling in the center of each dough circle
Fold and seal the edges of each filled circle to form a small crescent or half-moon shape; repeat with the remaining circles, then gather and re-roll the scraps to cut more circles until you get about 14 crescents.
Transfer the crescents to a baking tray lined with parchment paper, whisk the egg white with a fork, and brush each crescent lightly using a pastry brush.
Finely chop the remaining walnuts with a knife, sprinkle a few pieces over each crescent, then bake at 340–350°F (170°C) for about 15 minutes, until lightly golden.
The walnut and jam crescents are ready; arrange them on a serving plate and enjoy these tender, fluffy cookies while slightly warm or at room temperature.