Scoop a few tablespoons of dough (about 2 ounces) onto your palm and roll into a smooth ball. Place the ball in between two pieces of plastic wrap and using a rolling pin, gently press the dough into a circle. (It's ok if the dough cracks a bit around the edges, but if it cracks completely that means it's not moist enough. You can fix it by adding a splash of water to the balls of dough, kneading it in and then re-rolling it. Not a fun solution but I've done this and it works great.)
Place a teaspoon or two on one half of the dough circle. Using the bottom plastic wrap, lift and fold the dough over, creating a half moon shape. Using the tines of a fork, crimp the edges tightly and if you're really fancy, you can trim off any scraggly edges with a knife. Gently move the finished empanada to a cutting board and repeat this process until you've gone through all of the dough.
In a cast iron skillet (or medium pot), add enough vegetable oil until it reaches about 3 inches, and heat until a thermometer reaches 350F. If you don't have a thermometer, not that big of a deal--add a tiny bit of scraped dough and if it sizzles, it's ready for the empanadas. Carefully add three empanadas at a time, being sure to not overcrowd the pan. Cook for 2 to 4 minutes, until the empanadas are golden brown and crispy. Drain on a bed of paper towels and repeat until all of the empanadas are fried. Serve immediately with the aji.