Steps
Sauce:
Melt butter in a small saucepan over medium-low heat. Stir in allspice and transfer seasoned butter into a small bowl.
Grill:
Brush both sides of pineapple rings with seasoned butter. Grill directly over medium heat 8-10 minutes, turning occasionally. Brush pineapple with seasoned butter several times throughout grilling. Set aside.
Glaze:
Mix orange juice with cornstarch and stir until cornstarch is dissolved.
Add honey and lime juice to orange juice mixture. Simmer over medium-high heat until glaze begins to boil, cornstarch thickens and becomes clear.
Assemble:
Cut each grilled pineapple ring into 4 to 5 pieces. Place one scoop of ice cream into each serving bowl and top with grilled pineapple chunks. Spoon 1/4 of the glaze over ice cream and garnish with cherry.