1. Toast cumin and peppercorns in a skillet over medium heat, 2-3 minutes. Transfer to a small food processor along with oregano, cayenne, garlic, and 1 tbsp. salt. Process to a paste. Cut about twenty-five 1 1/2 inch-wide slits in the pork about 1 inch deep. Rub garlic paste all over pork, pressing it into slits. Transfer pork to a roasting pan. Whisk together orange juice, lime juice, oil, and 2 tbsp. salt in a bowl; pour over pork. Cover and refrigerate, turning occasionally, for 18-24 hours.
2. Remove pork from refrigerator 2 hours before you are ready to roast, to allow it to come to room temperature. Heat oven to 325F. Roast, basting every 30 minutes, until a meat thermometer inserted in thickest part of pork registers 160F, about 3 hours total. (Add 1 cup water to pan when liquid evaporates; cover loosely with foil if skin gets too dark.) Let rest for 15 minutes, then carve and serve.