On a floured surface, roll the pastry out a bit to even out the any folds and make it a touch thinner. Cut a 10-inch circle of dough from it, prick it, and keep it chilled.

Preheat oven to 425 degrees F.

Place a heavy 9 or 10-inch metal cake pan on the stove on a large burner and turn the heat onto medium. Add the butter and warm to melt it. Add the maple syrup and vanilla bean and bring to a boil stirring a bit. Remove the vanilla bean. Take the pan off the heat and place the banana slices in the pan decoratively in concentric circles to cover the whole bottom of the pan. Place the pastry over the bananas to cover them, tucking the pastry down along the inside of the pan. Later, during baking, the pastry will shrink to fit the pan.

Bake for 20 to 25 minutes until the pastry is golden brown. Let cool in the pan 30 minutes then warm the bottom of the pan on the stove for a minute and turn the tart out onto a serving platter.