Melt butter in a small saucepan over medium-low heat. Stir in allspice and transfer seasoned butter into a small bowl.
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.
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.
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.