Place chiles on a grill, under the broiler, or on a comal over medium heat. Roast, turning occasionally, until skins are blistered and charred (about 10–15 minutes). Place in a plastic bag or covered bowl to steam for 5 minutes, then peel, seed, and chop.
Heat olive oil in a skillet over medium heat. Sauté onion and garlic until soft, about 3 minutes.
Stir in flour and cook 1 minute.
Add roasted chiles, jalapeños (if using), and milk. Simmer 2–3 minutes, then stir in cheeses until melted.
Season with salt. Remove from heat and let cool slightly.
Empanada Dough
In a large bowl, combine flour and salt. Mix in lard with your fingers or a pastry cutter until crumbly. Add egg and beer, mixing until a smooth dough forms. If using a stand mixer, knead with the dough hook for 5 minutes; if by hand, knead until soft and elastic.
Assemble and Bake Empanadas
Preheat the oven to 350 degrees F.
Take out half the dough and split it into 12 equal balls of dough.
On a floured surface, roll out the dough balls into small round circles. Place a small dollop of filling on one half of each of the dough circles.
Wet the bottom edge of the circles with egg glaze to help seal the two halves. Fold over the dough to cover filling and seal off the edges with a fork pressing down along the edges or using a pastry cutter.
Repeat with remaining dough and filling.
Brush each empanada with egg glaze.
Puncture the top of each empanada with a fork to allow steam to escape while baking.
Place parchment paper on a cookie sheet; place the empanadas on the parchment paper and bake for 15 to 20 minutes on middle rack in the oven. If after 15 minutes you notice the bottoms of the empanadas starting to brown, move the cookie sheet to the top rack and continue to bake for the last 5 minutes, until golden brown.
Cool slightly before serving.
Video
Notes
No mixer? The dough can easily be kneaded by hand.
Make ahead: Refrigerate baked empanadas for up to 3 days. Reheat in a toaster oven or bake at 350°F for 8 minutes.
Cheese swaps: Try Monterey Jack or mozzarella if Oaxaca isn’t available.