Remove the top end of the pineapple by holding it firmly and twisting it off. Use a sharp serrated knife to trim off both ends of the pineapple. Set the pineapple on the bottom cut-end and, starting at the top, cut the skin off of the pineapple by following the curve of the fruit. Overlap your cuts to ensure that you cut out all of the eyes (the brown indentations on the pineapple).
Once all of the skin has been removed from the pineapple, slice the pineapple in half from the top down. Slice each half in half again, from the top down. Slice each quarter lengthwise into 3 wedges of equal size. Use your knife to cut the core out of each wedge so that you have a total of 12 trapezoidal shaped wedges.
Set 8 wedges aside, and take the remaining wedges and cut into small dice, about 1/4-inch cubes. You should have about 1 cup of small diced pineapple.
Preheat a grill to medium-high and spray or brush the grates with vegetable oil.
Lay the pineapple wedges on the grill and cook for 2 to 2 1/2 minutes. Rotate the pineapples 90 degrees and cook another 2 to 2 1/2 minutes. Turn onto the second side and cook 2 to 2 1/2 minutes longer. Turn onto the third side and cook a final 2 to2 1/2 minutes. Transfer grilled pineapple to a platter.
While the pineapple cooks, set a 10-inch grillproof saute pan on the grill and add 2 teaspoons of the butter. Once the butter melts, add the diced pineapples and saute, stirring occasionally, for 5 minutes. Add the sugar and cook until the sugar dissolves and starts to form large bubbles and turns golden, 6 to 8 minutes. Add the lime juice and swirl the pan to incorporate. Continue to cook for 3 minutes. Add the rum to the pan and tilt the pan to try and flame the rum. Cook for 3 minutes, then add the pineapple juice to the pan. Continue to cook until the liquid has reduced by half, 4 to 5 minutes longer. Remove from the heat and swirl the remaining 2 teaspoons of the butter into the sauce.
Pour the hot sauce over the grilled pineapple with the cross-hatched sides facing up. Garnish with the chopped mint. Serve with a scoop of vanilla ice cream if desired.