In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt.
In another bowl, combine buttermilk, egg, and vanilla extract.
Gradually add the wet mixture to the dry ingredients, stirring until just combined.
Cover the dough with plastic wrap and let it rest for about 30 minutes.
On a floured surface, roll out the dough to about 1/2 inch thick.
Cut the dough into squares or rectangles, about 2 inches wide.
Heat vegetable oil in a deep skillet or fryer to 350°F (175°C).
Carefully drop the cut pieces of dough into the hot oil, a few at a time.
Fry for about 2-3 minutes per side until golden brown, then transfer to paper towels to drain.
Dust with powdered sugar while still warm and serve immediately.