Preheat a grill pan or grill grate over medium heat.
Melt butter in a small saucepan over medium heat. Add the brown sugar, salt, and pumpkin pie spice. Bring to a boil, stirring until the sugar has completely dissolved. Simmer until mixture thickens about 5 minutes. Remove from heat, stir in the vanilla and set aside.
Cut each banana lengthwise, leaving the skin on and brush with butter and brown sugar sauce.
Oil the grill pan and arrange the bananas, cut side down, on the pan. Grill until caramelized, about 4 minutes. Turn the bananas and grill until the skins are blackened bananas are soft and warmed through, about 5 minutes more. Baste frequently with the sauce during the cooking process.
Remove from grill to a serving platter and serve with a scoop of vanilla ice-cream, drizzled with remaining sauce.