Preheat the oven to 350°F (175°C).
Line baking sheets with parchment paper.
In a large mixing bowl, combine the flour, powdered sugar, baking powder, and salt.
Add the oil, softened butter, and water.
Mix by hand until a soft, smooth dough forms. Avoid overmixing.
Divide the dough into three equal portions.
Place one portion of dough between two sheets of parchment paper and roll into a thin rectangle.
Remove the top sheet of parchment and spread a thin layer of your desired filling over the dough.
Starting from the long edge, gently roll the dough into a log, jelly-roll style.
Slice into individual cookies, about 1 inch thick.
Place on the prepared baking sheet, leaving a little space between cookies.
Bake for 18–20 minutes, or until the bottoms are lightly golden.
Cool slightly, then generously dust with powdered sugar.