In a food processor, combine the flour, salt, baking powder, and sugar, then pulse a few times.
Add the butter and pulse until the mixture resembles wet sand.
Add the ricotta cheese and vanilla extract, then pulse just until the dough comes together.
Transfer the dough to a floured surface and press it into a smooth ball. Wrap in plastic wrap and place in the freezer while preheating the oven to 355F (180C). Line a baking sheet with parchment paper.
Roll out the dough on a floured surface to ⅛ inch (3mm) thickness. Use a 3-inch (8cm) cookie cutter to cut out 14 discs, gathering and rerolling scraps as needed.
Pour some granulated sugar onto a small plate. Press one dough disc into the sugar, coating one side. Lift the disc, fold it in half with the sugared side inside, then press one side of the half-moon shape into the sugar again. Fold it in half once more, forming a triangle with the sugared side inside. Finally, dip one side of the triangle in sugar and place it on the prepared baking sheet, sugar side up. Repeat with the remaining dough discs.
Bake for 20-25 minutes, or until golden brown around the edges and on top.
Remove from the oven and allow the cookies to cool on a wire rack before serving.