Preheat the oven to 375 degrees F (190 degrees C). Line 2 baking sheets with parchment paper.

Sift together flour, sugar, and salt into a large bowl. Cut in chilled butter with a pastry blender or 2 knives until mixture resembles small peas. Add vanilla. Mix in cold water, 1 tablespoon at a time, until dough comes together and forms a ball.

Divide dough into 2 pieces and wrap with plastic wrap; chill in the refrigerator until firm, at least 1 hour.

Meanwhile, make filling: Beat together butter, sugar, and cinnamon in a bowl until well combined.

Roll out dough on a lightly floured work surface to 1/2-inch thickness. Cut dough into rectangles with a knife. Drop 1 tablespoon filling onto 1/2 of the rectangles. Cover with remaining rectangles. Press the edges with a fork to seal. Poke a few holes in the top of each pastry with a toothpick.

Arrange pastries on the prepared baking sheets.

Bake in the preheated oven until golden brown, 25 to 30 minutes. Cool pastries on a wire rack, about 15 minutes.