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To make the filling: Place the tomatillos, garlic cloves, and jalapeño(s) in a pot and cover with cold water. Cover the pot, place it over high heat, and bring the water to a boil. Bring the water down to a simmer and cook until the tomatillos are tender, soft, and pale green, about 10 minutes.
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Remove the pot from the heat and transfer the tomatillos, garlic, and jalapeño(s) to a blender or food processor, along with 2 tablespoons (28g) of the cooking liquid, the onion, cilantro, lime juice, and salt. Blend the ingredients until nearly smooth, adding more water a teaspoon or two at a time if necessary to facilitate blending.
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Pour the salsa into a saucepan and bring it to a simmer over medium-high heat. Reduce the heat to medium and simmer the salsa for 6 to 8 minutes, until it’s reduced and thickened slightly and has turned a deeper shade of green.
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Remove the salsa from the heat and set it aside to cool to room temperature.
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Pour about 1 cup (236g) of salsa into a large bowl, and stir in the shredded chicken and cheese. Set aside the filling while you prepare the dough. You’ll serve the remaining salsa alongside the empanadas.
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To make the dough: Weigh your masa harina; or measure it by gently spooning it into a cup, then sweeping off any excess. In a large, shallow bowl, whisk together the masa harina and salt. Gradually add the warm water, stirring with your hands to make a cohesive dough.
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Using your hands, mix and knead the dough in the bowl for a minute or so, until it’s smooth and somewhat firm; it should feel like Play-Doh. If the dough sticks to your hands and feels wet, add more masa harina a teaspoon to a tablespoon at a time. If you roll a piece into a ball and squeeze it and the edges crack, add more water a teaspoon to a tablespoon at a time.
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To shape and fill the empanadas: Cut two round or square pieces of food-safe plastic — from a plastic produce or zip-top bag — to a size about 1/2" larger than the diameter of your tortilla press. Set aside.
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Divide the dough into 12 pieces (45g to 50g each) and roll each piece into a ball. Place the balls on a clean work surface and cover them with plastic or a damp kitchen towel to keep them moist.
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Working with one ball of dough at a time, sandwich it in the center of the two pieces of plastic. Place the plastic-enclosed dough on the bottom plate of a tortilla press. Gently squeeze the handle of the press until the dough is about 1/8” thick and 4 1/2” to 5” in diameter. To achieve a nicely rounded tortilla, jiggle the handle of your press just as you near the bottom. You may need to press it a couple of times to reach the desired thinness.
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Remove the dough circle from the press and peel off the top piece of plastic. Spoon about 2 tablespoons of filling onto the center of the dough, then use the bottom piece of plastic to help fold the dough in half to form a semicircle. Pinch the edges with your fingers to seal the filling inside.
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Place the empanada on a parchment-lined or lightly greased baking sheet, cover with plastic or a damp kitchen towel, and set aside while you form the remaining empanadas.
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To fry the empanadas: Pour the vegetable oil into a heavy-bottomed skillet or pot; you’ll need enough oil to fill the bottom 1” of your vessel. Heat the oil over medium-high heat until it reaches 375°F on a digital or frying thermometer.
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Carefully place as many empanadas into the hot oil as will fit without overcrowding.
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Fry the empanadas until crispy and golden, 2 to 4 minutes per side. Remove the empanadas from the oil and place them on a paper towel-lined baking sheet to drain away any excess oil. Put the pan in a low (200°F) oven to keep the empanadas warm.
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Repeat with the remaining empanadas.
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Serve empanadas warm with the extra salsa verde, sour cream, and/or any other garnishes you desire.
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Storage information: Store leftover empanadas, well wrapped, in the refrigerator for several days; reheat in a hot pan or low oven to serve.
