In a large bowl, whisk together the flour, sugar, salt, and baking powder.
Add the cold butter cubes. Cut them into the flour with a pastry blender or fork until the mixture looks like coarse crumbs.
In a medium bowl, whisk together the egg, milk, and vanilla.
Pour the wet mixture into the flour mixture and stir just until a soft dough forms. If it seems dry, add a small splash more milk. The dough should come together without feeling sticky.
Turn the dough out onto a lightly floured surface and shape it into a square. Wrap tightly in plastic wrap and refrigerate at least 2 hours or overnight.
Roll the chilled dough out on a lightly floured surface to about 1/8 inch thick. Cut into 5 to 6 inch circles.
Spoon 1 to 2 tablespoons of cherry pie filling into the center of each circle. Fold the dough over into a half-moon shape and press the edges together firmly, then crimp with a fork or pie press to seal.
Pour about 2 inches of oil into a deep skillet or heavy pot and heat it to 350 degrees F.
Fry the pies in batches for 1 to 2 minutes per side, until golden brown. Do not crowd the pan.
Lift the pies out with a slotted spoon and drain them on paper towels.
Let the pies cool slightly, then dust with powdered sugar or drizzle with glaze if you like.