Select a ripe pineapple by turning it upside and smelling it. If it smells sweet when it’s held in front of your nose, select that one. Using a knife, cut the top and bottom off of the pineapple. Next, cut away all of the outer peel. With the pineapple standing up, cut it vertically into four sections, cut off the core from each section. Next, cut each section into slices about an inch thick, that way you get more broiled surface and you don’t kill your blender.
Spread the slices out on a cookie sheet and sprinkle with sugar. Using a torch or the broiler of your oven, caramelize the sugar until it is brown and bubbly. Set aside to cool slightly. Add the pineapple, vanilla, and only enough water to make blending easy, to your blender. Blend until the pineapple is pureed and strain into a pitcher. Add water as needed to get the right consistency without diluting the flavor too much. Taste for sugar and add more if desired (this really depends on the sweetness of the pineapple). Stir in juice of 1 lime and 2 cups of rum. Chill until ready to drink. Serve over ice.