Add the eggs, granulated sugar, and vanilla to a mixing bowl. Beat until well combined and slightly lightened.
Stir in the sour cream.
Gradually add all-purpose flour and a small amount of baking soda, mixing until a soft dough forms that can be rolled out. Avoid adding more flour than necessary.
Transfer the dough to a lightly floured work surface and roll it out thinly.
Cut the rolled dough into strips or small elongated pieces.
Shape the pieces into traditional žagariņi. A classic method is to cut a short slit through the center of each piece and pull one end through the opening to create a twisted shape.
Heat frying oil or fat in a deep, heavy-bottomed pan to approximately 175–180°C / 350–355°F.
Fry the pastries in small batches until puffed and golden brown, turning as necessary so they cook evenly.
Remove with a slotted spoon and drain on paper towels or a wire rack.
While still slightly warm, dust generously with powdered sugar.
Allow to cool and serve.