Step 1

Make a ½"-deep cut along each side of each drumstick (this will help the marinade penetrate quickly into the flesh) and place in a large bowl; set aside while you make the marinade.

Step 2

Purée shallots, garlic, coconut cream, lime juice, salt, red pepper flakes, shrimp paste, half of the pineapple slices, and 2 Tbsp. oil in a blender to a smooth paste. Set 1 cup marinade aside; pour remaining marinade over reserved drumsticks. Toss until drumsticks are completely coated in marinade. Let sit 15 minutes.

Step 3

Prepare a grill for medium indirect heat (for a charcoal grill, bank coals on one side of grill; for a gas grill, leave one or two burners off). Lightly oil grate; arrange drumsticks over indirect heat. Baste chicken with reserved marinade, then cover and grill 20 minutes.

Step 4

Uncover grill and turn drumsticks over. Baste one more time with marinade, then cover and grill until drumsticks are golden brown and an instant-read thermometer inserted into the thickest part of a drumstick registers 165°, 25–30 minutes.

Step 5

Move drumsticks over direct heat and grill, turning halfway through, until golden brown and charred in spots, about 4 minutes. Transfer drumsticks to a large platter.

Step 6

Arrange remaining pineapple slices on grate over direct heat and grill, turning halfway through, until golden brown and lightly charred in spots, about 5 minutes. Remove from heat and arrange over and around drumsticks.

Step 7

Top pineapple and drumsticks with cilantro and serve with lime wedges for squeezing over.