Peel and core pineapples. Cut into 6 (1 1/2-inch-thick) rings. Set aside.
Beat butter and sugars at medium speed with an electric mixer until creamy. Add rum, cinnamon, and salt; beat well.
Divide butter mixture into 6 (6-inch) cast-iron skillets. Place over medium-high heat until butter melts. Add 1 slice of pineapple and, if desired, half of a vanilla bean to each skillet. Cook until pineapple caramelizes on bottom; flip and repeat procedure. Keep warm.
Roll out puff pastry to 1/4-inch thickness. Cut 3 (7 1/2-inch) circles out of each sheet. Place 1 circle over each pineapple slice, and tuck in edges. Repeat procedure with remaining pastry sheet. Bake at 400° for 20 minutes or until golden brown.
Remove from oven, and let stand 5 minutes. Place plate upside down over top of pan, and carefully invert tart onto plate. Repeat process with remaining skillets. Top each with a scoop of vanilla ice cream, if desired. Serve immediately.
Note: If substituting 1 (12-inch) skillet, use only 4 pineapple slices, 3/4 cup butter, and half amounts of the remaining ingredients. Use 1 pastry sheet to cover all slices. After baking, invert tart onto platter. Cut in wedges.