Pork Volcánes al Pastor

Directions

1. 1
   Place pork shoulder on a parchment-lined rimmed baking sheet and freeze, uncovered, until almost completely frozen, about 2 hours. Using a very sharp knife, thinly slice pork (shoot for about ⅛" thick).
2. 2
   Transfer to a large bowl.
3. 3
   Meanwhile, bring guajillo and morita chiles and 1 cup water to a boil in a medium saucepan. Cover, remove from heat, and let sit 30 minutes to allow chiles to soften.
4. 4
   Transfer chiles and soaking liquid to a blender.
5. 5
   Add garlic, orange juice, lime juice, achiote paste, and salt; purée until smooth.
6. 6
   Pour over pork and toss to coat. Cover and let sit at room temperature 2 hours, or chill up to 6 hours.
7. 7
   Place a rack in middle of oven; preheat to 350°. Evenly space out tortillas on a baking sheet and bake until lightly toasted and very crisp (edges will curl and pucker), 35–45 minutes.
8. 8
   Heat 1 Tbsp. oil in a large nonstick skillet over high until smoking.
9. 9
   Spread about one-fourth of pork across skillet in a single layer; cook, undisturbed, until browned underneath, about 2 minutes. Turn over and cook, undisturbed, until browned underneath and cooked through, about 2 minutes.
10. 10
    Transfer to a platter and wipe out skillet. Working in 3 batches, repeat process with remaining pork and 3 Tbsp. oil.
11. 11
    Increase oven temperature to 500°. Divide pork among tostadas and top with quesillo; bake until cheese is melted, 8–10 minutes. Top with onion and cilantro and serve with lime wedges.