Trim and cut the pineapple.  Melt ½ stick of the butter in a large sauté pan over medium heat. Add the pineapple and a pinch of salt and cook until tender and starting to brown. Remove and place the pineapple in a bowl and add the brown sugar to the pan. Add more butter if necessary.  Cook the butter, brown sugar mixture until bubbling. Reduce the heat and add the balsamics. (The mixture will bubble up.) Stir the mixture to incorporate the balsamic vinegars.

Add the other half stick of butter and the heavy cream and simmer until reduced to a sauce consistency. Add the pineapple back to the pan and warm through. Place a scoop of ice cream in a bowl and top with the pineapple caramel mixture.