Sprinkle yeast over warm water in a bowl. Let stand until yeast softens and begins to form a creamy foam, about 5 minutes.

Meanwhile, combine flour and salt in the bowl of a food processor; pulse once or twice to combine. Scatter butter over flour; process until butter is thoroughly mixed into flour mixture, about 1 minute.

Whisk yeast mixture, sour cream, egg yolks, egg, and vanilla extract together in a bowl; pour into food processor. Pulse several times until dough starts to hold together and cleans the sides of the bowl (do not overmix). Divide dough into two, shape into disks, wrap in plastic, and refrigerate at least 2 hours to overnight.

Preheat the oven to 375°F (190°C). Line several baking sheets with parchment paper.

Sprinkle work surface generously with sugar. Roll out 1 dough disk into an 8x16-inch rectangle; sprinkle dough generously with sugar. Fold dough over in thirds, letter-style. Repeat rolling, sugaring, and folding two more times. Roll out dough into a 4x14-inch rectangle, about 1/4-inch thick. Repeat process with second dough disk.

Cut strips from short sides of dough rectangles about 1/2- to 3/4-inch wide. Place strips onto the prepared baking sheets, twisting and slightly stretching strips or forming into horseshoe shapes.