Preheat the oven to 225 degrees F. Line 2 baking sheets with silicone baking mats or parchment. Using a knife, remove the top of the pineapple and 1/2-inch of the bottom so it sits flat on your cutting board. Cut the skin off the pineapple from top to bottom in 2-inch strips. Using a small melon baller or teaspoon, remove all the eyes from the pineapple. Put the pineapple on its side and slice 12 rounds as thinly as possible. Put the slices on the baking sheets and bake until almost totally dry and lightly golden around the edges, about 3 hours. Remove from the oven and immediately transfer each flower to a muffin cup, pressing the center to the bottom. Let cool completely, 1 hour.
Combine the pineapple juice, rum, cream of coconut, ice and a pinch of salt in a blender and blend; it will make a nice frothy layer on top.
Pour into 4 tumblers and garnish with the pineapple flowers. The remaining flowers will keep in an airtight container at room temperature up to 2 weeks.
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