Prep time: 20 minutes
Cook time: 5 hours 8 minutes
Total Time: 5 hours 28 minutes (plus resting time)
1. For topping: Place pork in a resealable bag. Add oil, oregano, lime juice, garlic, cumin, pepper and salt and massage into pork to cover completely. Marinate refrigerated for up to 2 hours or overnight. Brush excess marinade off pork.
2. Preheat oven to 300°F and line a rimmed baking sheet with aluminum foil. Place pork, fat-side-up, on the prepared baking sheet. Cover with aluminum foil. Roast until tender and pork easily pulls apart, about 4-5 hours. Shred pork into bite-sized pieces using forks. Set aside for topping pizza.
3. For crust: Generously grease a large bowl with olive oil and set aside. Combine water, sugar and yeast in the bowl of a stand mixer fitted with a dough hook attachment. Mix on low speed until combined, about 30 seconds. Let stand until yeast is foamy, about 5 minutes. Add flour and salt. Mix on medium speed until smooth dough is formed, about 3-6 minutes. Transfer dough to the prepared bowl and cover with plastic wrap. Let rest until doubled in size, about 1 hour 30 minutes.
4. Place pizza stone in the oven and preheat to 500°F. On a lightly floured surface, press dough into a 14-inch round circle. Transfer dough round to lightly floured pizza peel. Top with Swiss cheese, 1 1/2 cups pulled pork, ham and pickled chips, leaving a 1/2-inch border. Quickly slide pizza onto preheated pizza stone. Bake, rotating pizza halfway through, until crust is golden brown and cheese is melted, about 5-8 minutes.
5. Meanwhile, in a small bowl, combine mayonnaise and mustard. Drizzle mayonnaise mixture over pizza and top with cilantro. Slice and serve.
Tip: Use leftover pork to make Cubano sandwiches!