In a medium-sized baking bowl, combine flour, baking powder and salt. Using a fork (or your hands), mix in Greek yogurt until crumbly. From here, use your hands to knead the dough into a ball. You want the dough to still have moisture, but not stick to your hands.
Sprinkle extra flour on a clean surface and roll out dough until it’s very thin (as if you were making a thin-crust pizza). Using a glass, small bowl, or cookie cutter, cut out as many rounds as you can. Roll remaining dough back out and form into more rounds (like you would when making Christmas cookies). I got 14 rounds using a tall pint glass. I then roll each circle out just a tad more. You could also gently do this with your hands like you would with pizza dough.
Fill each circle with filling of choice and brush edges of dough with the egg wash. Fold one edge over to the other and crimp with a fork to seal.
Place assembled empanadas on a parchment-lined baking sheet. Brush tops of empanadas with remaining egg wash, then bake in a 375-degree oven for 22-25 minutes, or until golden brown on top.