In a large bowl, whisk together 3cupsall-purpose flourplus more for surface, 1teaspoonkosher salt, and 1teaspoonbaking powder. Add 1/2cupcold buttercut into cubes and work it into the flour with your hands or a pastry cutter until the mixture resembles pea-sized granules.
Add 3/4cupwater and 1large egg to the flour mixture and mix until a dough forms. Turn the dough out onto a lightly floured surface and knead until smooth, about 5 minutes. Wrap the dough in plastic wrap and refrigerate for at least 1 hour.
While the dough chills (or after it has chilled), make the filling: heat 2tablespoonsextra-virgin olive oil in a large cast-iron or nonstick skillet over medium heat.
Add 1yellow onion (chopped) and cook until soft, about 3–5 minutes. Add 4clovesgarlic (minced) and cook until fragrant, about 1 minute.
Add 1lb.ground beef and cook, breaking it up with a spoon, until no longer pink, about 5–7 minutes. Drain any excess fat from the pan.
Return the pan to medium heat and stir in 1tablespoontomato paste, 1teaspoondried oregano, 1teaspoondried parsley, 1teaspooncumin, and 1/2teaspoonsmoked paprika. Season with kosher salt and freshly ground black pepper to taste. Add 1/2cupchopped tomatoes and 1/2cupdiced green chiles and cook about 3–5 minutes. Remove from heat and let the filling cool slightly.
Remove the chilled dough and place it on a lightly floured surface. Divide the dough in half. Roll one half out to 1/4-inch thickness. Using a 4.5-inch round cookie cutter or a cup, cut out rounds. Repeat with the remaining dough.
Lightly moisten the outer edge of each dough round with water. Place about 2 tablespoons of the beef filling in the center of each round. Top the filling with shredded Cheddar and Shredded Monterey Jack.
Fold each dough round in half over the filling to form a half-moon. Press the edges together, then crimp the edges with a fork to seal. Repeat until all empanadas are assembled.
Preheat the air fryer to 400°F.
Brush each empanada with egg wash. Place empanadas in a parchment-lined air fryer basket in a single layer, making sure they do not touch (cook in batches as needed). Air fry for 10–12 minutes, or until golden brown. If desired, rotate the basket or turn the empanadas halfway through for even browning.
Transfer cooked empanadas to a rack, garnish with freshly chopped cilantro, and serve with sour cream for dipping.