1. Let pork stand at room temperature 30 minutes.
2. Pulse 1/3 cup garlic, 1/4 cup juice, oregano, cumin, and salt together in a food processor until mixture is almost smooth.
3. Preheat oven to 375 degree F. Lightly oil a large heavy roasting pan. Rinse and pat pan and cut 1-inch slits in top, about 2 inches apart. Pour garlic mixture over pork and, with fingers, push some of mixture into slits. Pour 1/4 cup juice and 1/4 cup water around pork in pan. Cover with heavy-duty aluminum foil, tenting in center so it is not touching pork, and seal edges around sides of pan. Roast pork in middle of oven 30 minutes.
4. Carefully lift 1 corner of foil, avoiding steam, and pour in remaining 1/4 cup juice and the vinegar. Reseal and roast, basting once, 2 hours (adding water, as needed, to bottom of pan if dry).
5. Remove foil and baste pork with pan juices. Roast, uncovered, until pork is fork-tender and skin is crisp, 1 to 1-1/4 hours more. Transfer pork in pan to rack; let stand 15 minutes before carving into 1/4-inch-thick slices.
6. Meanwhile, to make sofrito, pulse onion, bell pepper, cilantro, and remaining 1 tablespoon garlic together in a food processor until smooth. Heat oil in a large saucepan over moderate heat. Add onion mixture and cook, stirring, 2 minutes. Transfer to a serving bowl, leaving 1/3 cup sofrito in saucepan (reserve sofrito in bowl for sauce). Add 3-1/4 cups water to sofrito in saucepan and bring to boil; stir in rice. Immediately reduce heat to low, cover, and cook 20 minutes. Remove from heat and let stand, covered, 5 minutes. Fluff rice with a fork and season with salt before serving.
7. Serve pork with sofrito rice, sauce, and pan juices. Makes 8 servings.