Preheat the broiler and line a baking sheet with foil. Halve the tomatillos and place them cut-side down on the foil. Broil until softened and lightly charred in spots, 3 to 4 minutes. Flip and broil again until golden brown but not black (the tomatillos should be tender but not mushy), 2 to 3 minutes more. Transfer to a cutting board, cool slightly, then chop the tomatillos coarsely.
While the tomatillos are broiling, stand the ear of corn in a bowl with a flat bottom and slice the kernels off right into the bowl. Grate the cheese on top of the corn. Add the chopped tomatillos and a big pinch of salt, and then toss to combine.
Heat the oil in a 10-inch, high-sided skillet over medium heat until a deep-fry thermometer inserted in the oil registers 340 degrees F.
Have a little bowl of cool water on hand. Lay the empanada wrappers on a cutting board. Place 2 heaping tablespoons of the tomatillo filling in a short strip in the center of one wrapper. Then brush a little water on the bottom edge of the wrapper and fold the top half over, creating a half-moon shape. Press to seal with your fingers, and then crimp the edges with a fork. Repeat with the remaining filling and wrappers.
Fry the empanadas, 5 at a time, until golden brown, 5 to 6 minutes. Flip and fry until deep golden brown, another 2 to 3 minutes. Drain on a rack and serve immediately.
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