In a medium bowl, stir together the all-purpose flour, kosher salt, and 1 tablespoon canola oil. The mixture will look crumbly.
Add the cold water 1 tablespoon at a time, stirring after each addition, until the dough is soft and cohesive. Up to ½ cup is typical, but flour measurement and humidity can affect the amount, so you may not need it all.
Shape the dough into a disk, wrap it tightly in plastic wrap, and refrigerate for at least 30 minutes.
Cut the chilled dough disk into 8 equal wedges. On a lightly floured surface, roll each piece into a circle about 4 inches wide.
Place 1 heaping tablespoon of shredded cheese in the center of each circle, leaving the edge clean. Moisten the edge of one half with water, fold the dough over the filling, gently press out as much excess air as possible, and press the edges firmly together to seal; no fork crimp is needed.
To pan-fry: Add canola oil to a large, heavy-bottomed skillet to a depth of about ¼ inch—roughly 1–2 cups, depending on the skillet. Heat over medium-high heat to 350°F. Working in batches without crowding the pan, fry the empanadas for 2–3 minutes per side, until crisp and golden brown.
To air-fry: Preheat the air fryer to 400°F and coat the basket with cooking spray. Arrange the empanadas in a single layer without crowding, working in batches as needed. Air-fry for 3 minutes, flip, and cook for another 3–4 minutes, until crisp and lightly golden.
Serve warm with tomatillo salsa or your favorite dipping sauce. One serving is 2 empanadas.