Peel and core pineapple. Cut half of pineapple into bite-size pieces (about 1"); set aside. Chop remaining pineapple into small pieces and transfer to a small saucepan. Cook over low heat, stirring occasionally, until very soft and broken down and nearly all juice is evaporated, 15–18 minutes. Transfer to a blender and add ¼ cup water; purée until smooth.
Heat 2 tablespoons oil in a large Dutch oven or other heavy pot over medium-high. Lightly season pork with salt and pepper. Working in 2 batches, cook pork until well browned on all sides, 5–8 minutes per batch. Transfer to a plate.
Reduce heat to medium-low and add onion. Cook, stirring often, until fragrant and softened, about 5 minutes. Add garlic and cook until fragrant.
Return pork to pot and stir in pineapple purée. Add vinegar, soy sauce, oyster sauce, peppercorns, bay leaves, and ¾ cup water and stir to combine. Bring to a simmer and cover pot. Reduce heat so adobo is at a very gentle simmer and cook until pork is tender, 45–50 minutes.
Meanwhile, heat remaining 2 teaspoons oil in a large skillet over medium-high. Cook reserved bite-size pineapple pieces, tossing occasionally, until golden brown all over, 5–8 minutes. Transfer to a plate.
Uncover pot and skim off any fat from surface. Increase heat to medium and cook, uncovered, until sauce is thick and shiny, about 15 minutes. Gently stir in caramelized pineapple. Remove and discard bay leaves.
Serve pork adobo over rice, topped with scallions.