Combine butter, sour cream, 5 tablespoons sugar, and egg yolks in the bowl of a food processor fitted with the dough blade; process until combined. Add flour and yeast; process until dough comes together. The dough should be moist and easy to work with. If dough feels too wet, add a little more flour; if it's too dry, add milk, 1 tablespoon at a time. Shape dough into a ball, cover with a damp towel, and set aside.

Heat 1 cup milk and 1 cup sugar in a saucepan until sugar dissolves and mixture has a syrupy consistency. Add chopped walnuts; stir to combine. Off heat; stir in raisins and lemon zest; cool filling.

Divide dough into 3 pieces. Roll out 1 dough piece on a lightly floured surface to form a long rectangle about ¼-inch thick; keep remaining dough covered. Spread ⅓ walnut filling on dough rectangle, leaving about 1 inch dough at edges. Roll up dough to form a log; press to seal. Place dough log, seam-side down, on a parchment-lined baking sheet. Repeat with the remaining dough and filling.

Beat egg and 1 tablespoon water together in a small bowl; brush logs with egg wash. Let rest for 1 hour in a warm place until dough has risen. Brush logs with egg wash; place baking sheet in the refrigerator for 30 minutes (this will give the dough a shiny finish).

Preheat the oven to 375 degrees F (190 degrees C).

Bake in the preheated oven until beigli are deep golden brown, 35 to 45 minutes.