Preheat the oven to 400 degrees F. Grease a 12-portion nonstick muffin tin with melted butter.
Cut circles out of the pie crusts using a 3 1/2-inch plain cutter and transfer them to the cups of the muffin tin. Press the dough evenly into the edges of each muffin cup, lining the sides. Whisk the milk, confectioners' sugar, egg yolks and egg together in a large glass measuring cup until smooth.
Carefully pour the milk-sugar mixture into each crust, leaving 1/8 inch at the top. Bake in the center of the oven until the pastry begins to brown, the filling is set but still jiggles, and a toothpick inserted into the center of a tart comes out clean, 12 to 15 minutes. Cool in the pan for 10 minutes before removing.
Meanwhile, combine the brown sugar with 2 tablespoons water in a small saucepan over medium heat and stir until completely melted. Stir in the butter and cinnamon until melted and smooth. Remove from the heat and cool.
To serve, arrange about 5 banana slices on top of each tart, overlapping them in a flower petal pattern. Serve the tarts immediately with caramel sauce drizzled over the top.