Whisk together the honey, sugar, lemon juice, rum, if using, vanilla bean paste, cinnamon, ginger and salt in a small bowl. Place pineapple rings in a large, shallow dish and pour marinade over. Allow to sit for 30 minutes at room temperature to macerate.
Meanwhile, preheat oven to 350 degrees F and preheat a grill or grill pan for cooking over medium-high heat. Grease a 12-inch metal fry pan or cast-iron skillet with butter.
Remove the pineapple rings from the maceration liquid and reserve liquid. Oil the grill grates. Place the pineapple rings on the grill and cook until slightly charred, 2 to 3 minutes per side. Remove from grill and let cool slightly before cutting 6 of the rings in to half-moons, leaving one ring intact.
Prepare the cake mix according to the manufacturer's instructions.
Place the intact pineapple ring in the center of the greased skillet. Lay the halved rings around the central ring, all facing the same direction. Pour half of the maceration liquid into the pan over the pineapple. Pour the cake batter over.
Bake, rotating the skillet halfway through, until top is golden and cake springs back when pressed, 40 to 50 minutes. Cool until just slightly warm, then carefully invert onto a cutting board or large platter. Slice and drizzle with remaining maceration liquid, then serve with vanilla ice cream.