Heat an oven-proof skillet over medium heat. Sprinkle white sugar evenly into the bottom of the skillet; cook until sugar melts and turns golden brown, about 1 minute. Reduce heat to low and stir butter into sugar. Stir cinnamon into butter mixture and remove from heat.
Dip each plantain slice into butter mixture to coat on both sides. Arrange coated plantains in a shingled pattern to cover the bottom of the skillet.
Spread puff pastry sheet over plantains, tucking corners into the skillet.
Bake in the preheated oven until puff pastry is golden brown, 30 to 35 minutes. Remove from oven and cool briefly. Place a serving plate upside-down over the top of the skillet; flip the skillet to remove tarte tatin from the pan.
Whisk mascarpone cheese and confectioners' sugar together in a bowl until smooth. Spread a large dollop of mascarpone mixture over the top of the plantains. Serve with remaining mascarpone mixture on the side.