Toss shrimp with 2 tablespoons oil and 1/2 teaspoon each salt and pepper. Heat grill pan, grill, or broiler. Brush pineapple with 1 tablespoon oil. Grill or broil (in batches on rimmed baking sheets) until pineapple is slightly charred and shrimp are opaque throughout, about 3 minutes per side on the grill or 6 to 8 minutes in broiler (rotating pan and turning food over halfway through). If desired, set aside half of shrimp for the No-Cook Shrimp Rolls and refrigerate until ready to use.