Start the beef filling:

Bring 5 cups water to a simmer in a small pot (about 2 quarts) over medium-high heat. Meanwhile, cut 1 1/2 pounds flank steak crosswise into 4- to 6-inch pieces. Cut across the grain into 3- to 4-inch wide pieces. Cut the top off 1 garlic head to expose the cloves.
Add the beef, garlic, and 1/2 peeled small white onion (reserve the remaining onion for topping) to the simmering water. Bring to a boil, skimming off any foam from the surface as needed. Add 1 tablespoon kosher salt. Simmer, adjusting the heat as needed, until the beef is fork-tender, 1 hour to 1 hour and 40 minutes. Meanwhile, prepare the chiles.
Prepare the chiles:

Toast 2 dried ancho chiles and 1 dried California chile: If you have a gas stove, turn a burner on to medium heat. Toast each chile one at a time by holding it with tongs directly on the flame, turning occasionally, until fragrant, darkened in color, and starting to soften, 8 to 10 seconds per side. If you have an electric stove, toast the chiles in a frying pan over medium heat, about 2 minutes. Set aside until cool enough to handle.
Cut the stems off with kitchen shears, then remove and discard the stems, seeds, and veins. Place in a medium bowl and add enough warm water to cover. Add 1 teaspoon kosher salt and 1/4 teaspoon distilled white vinegar. Let the chiles soak until they soften, 15 to 20 minutes. Remove from the soaking liquid.
Finish the beef filling:

Add 1 1/2 teaspoons dried oregano to the beef, stir to combine, and remove the pot from the heat. Cover and let sit for 15 minutes.
Transfer the beef to a plate or clean cutting board. Shred with 2 forks into bite-size pieces, discarding any fat. Cover to keep warm. Pour the cooking liquid through a fine-mesh strainer set over a heatproof bowl or liquid measuring cup. Discard the contents of the strainer. Reserve the cooking liquid for the enchilada sauce.
Make the sauce:

Place the soaked chiles, 1 cup of the beef cooking liquid, 1/3 cup whole or 2% milk, 1 peeled garlic clove, 1 1/2 teaspoons vegetable or canola oil, 1 teaspoon cornstarch, and 1/4 teaspoon ground cinnamon in a blender. Blend until smooth, about 1 minute.
Pour into a medium frying pan and bring to a simmer over medium heat. Reduce the heat to low heat to keep warm.
Assemble the enchiladas:

Thinly slice the reserved 1/2 small white onion (about 1/2 cup). Crumble cotija or shred queso asadero cheese until you have about 1/4 cup.
Warm 12 to 14 corn tortillas if desired (or you can skip straight to frying them): Place on a comal, griddle, or pan, over a medium flame on a gas stove or outdoor grill, or in a skillet over medium heat on an electric stove. Cook, flipping occasionally, until it inflates with pockets of air, chars in spots, and is pliable. Stack together and wrap in a clean kitchen towel to keep warm.
Heat 1 1/2 cups vegetable or canola oil in a large saucepan over medium heat until 350ºF to 365ºF. Fry the tortillas one at a time: Add to the hot oil with tongs and fry until starting to soften and pliable but not crisp or browned, 10 to 15 seconds per side. Stack them on a plate.
Dip a tortilla in the enchilada sauce and flip, making sure the tortilla is fully coated. Place on a second plate. Repeat dipping, stacking the tortillas on top of each other, until you have 6 or 7. Place scant 1/4 cup of the beef filling down the center of the top tortilla. Roll the tortilla up over the filling and place seam-side down on a plate. Repeat with the remaining dipped tortillas.
Repeat dipping and filling the remaining tortillas. Serve topped with the onions and cotija or queso asadero cheese.