To make the al pastor, in a food processor, combine the pineapple juice, vinegar, garlic, oregano, paprika, salt, cumin, black pepper, cloves, and chiles and blend until smooth.
Place the pork shoulder in a bowl and pour in the mixture from the food processor. Fold to combine, cover, and let marinate for 4 hours or overnight.
Heat a grill pan or skillet over medium high heat. Use tongs to lift the pork out of the marinade and grill in batches until browned and cooked through. Also grill 8 of the pineapple rings until charred.
Transfer the pork and pineapple to a cutting board and chop the pineapple into bite sized pieces.
Preheat the oven to 500ºf with a pizza stone if you have one.
On a floured surface, divide the pizza dough in half and roll each into a 14” round, dusting with flour as needed.
Transfer to a baking sheet or parchment paper.
Top each pizza with ¼ cup tomatillo salsa, about 5 oz queso fresco, 5 oz oaxaca cheese, and ½ of the al pastor and pineapple.
Bake for about 9-12 minutes, or until crust is golden and cheese has brown splotchy marks.
Top with a splatter of salsa, cilantro, onions, lime, and reserved queso fresco.
Slice and enjoy!
