How to Make It
Preheat the oven to 400°. In each of two 10-inch ovenproof skillets, stir 3/4 cup of the sugar with 2 tablespoons of the water. Cook over moderately high heat, stirring occasionally, until a light amber caramel forms. Remove the skillets from the heat, add 2 tablespoons of butter to each and stir until combined.
Slice the bananas 1/2 inch thick. Carefully arrange the bananas in the skillets in overlapping concentric circles, working from the edges to the center.
On a lightly floured surface, roll out the puff pastry 1/4 inch thick. Using a pot lid or plate as a template, cut out two 10-inch rounds. Poke the pastry all over with a fork and lay the rounds over the bananas. Lightly brush the pastry with the egg wash. Bake the tarts in the upper and lower third of the oven for about 40 minutes, or until the pastry is golden brown and puffed and the filling is bubbling. Shift the pans from top to bottom during baking for even browning.
Run the tip of a knife around the edge of each tart to loosen the crust. Let the pans stand for 10 minutes. Working with 1 skillet at a time, set a skillet over moderate heat for 10 seconds. Invert a plate over the skillet, then carefully flip both the plate and skillet. Tap lightly, then remove the skillet. Cut the tarts into wedges and serve.