Combine the brown sugar, salt, coriander, pepper, thyme, onion powder, allspice, cinnamon, and cayenne in a small bowl and stir to mix. Set the breasts in a baking dish and drizzle with the oil, rubbing it over the meat on both sides. Sprinkle the rub, garlic, and scallions on both sides of the chicken, patting the seasonings into the meat with your fingers. Refrigerate for 1 hour while you make the glaze and prepare the grill.

Combine the butter, brown sugar, rum, and pineapple juice in a heavy saucepan. Boil until syrupy, 7 to 10 minutes over medium-high heat. Don't worry if the mixture starts to separate. Whisk it vigorously to combine.

Heat a gas grill to high or prepare a hot charcoal fire. Scrub and oil the grill grate.

Arrange the chicken breasts on the grill at a 45-degree angle to the bars of the grate. Grill until the chicken has grill marks, about 2 minutes, and then rotate the breasts 90 degrees (to get a crosshatch of grill marks) and continue grilling for 2 to 4 minutes. Flip the chicken breasts and generously brush the cooked tops with glaze. Cook the second side the same way, for 4 to 6 minutes. Flip the chicken breasts again, brush with the glaze, and grill until the breasts are firm to the touch, another 1 to 2 minutes. Transfer the breasts to a platter. Serve at once, drizzled with any remaining glaze.