Heat all ingredients except the ground beef and potatoes in a pan over low heat. After 5 minutes, add the ground beef to the pan and smash it with the back of a spoon, incorporating the seasoned sauce as it cooks. Once meat is almost cooked (about 7 minutes), add the cooked potato cubes and increase the heat to medium-high. Stir while cooking until the meat is done (about 3 minutes): it should appear wet, but not saucy. Remove from heat and let cool.
Whisk together the corn flours, salt and sugar. Add one cup of the warm water and mix with your hands to incorporate. Add the remaining water a little at a time until the dough holds together and is just slightly sticky, reserving enough to wet your hands to prevent sticking as you mix. Form into a ball and knead for about 2 minutes, wetting your hands as needed.
Divide the dough into 12 golf-ball size portions and roll each one into a sphere. Press each ball flat between two pieces of waxed paper using a tortilla press.
Place a heaping tablespoon of meat in the center of the pressed dough atop a sheet of wax paper. Gently fold the dough in half, lifting the edges of the wax paper and pressing the dough together through the paper to form a seal around the meat. There will be about a half-inch of extra dough around the edge—score the edge with the lip of a cup, peel back the wax paper and remove any extra dough. (You can collect it, reform it into balls and press it to make more shells).
Heat 2 inches of canola or vegetable oil in a large skillet until it reaches 350 degrees. Fry the empanadas until golden brown, about 3 minutes. Work in batches to avoid crowding the skillet. Serve with cilantro sauce or pico de gallo.
Note: To freeze, wrap each empanada in wax paper and place in a sealed freezer bag. Frozen empanadas take a few extra minutes to fry, but they’ll turn out extra crispy.