How to Make It
Melt 1 stick of the butter in a large casserole. Add the sugar and cook over moderately high heat, stirring until pale gold but grainy, about 5 minutes. Add the apples and stir until bubbling.
Add the cinnamon and cook over moderately low heat, stirring occasionally, until the apples are broken down, about 40 minutes. Begin gently stirring from the bottom of the casserole and cook until the mixture is lightly caramelized, about 10 minutes longer. Transfer to a platter to cool.
Preheat the oven to 350°. Melt the remaining 3 sticks of butter in a medium saucepan; skim off the foam. Pour the melted butter into a small bowl, leaving any milk solids behind. Brush ten 4-inch ramekins with the melted butter.
Using a 4-inch round biscuit cutter, stamp out 10 disks from 10 of the bread slices; discard the trimmings. Brush the disks on both sides with melted butter and set them in the ramekins. Remove the crusts from the remaining slices of bread. Brush the slices on both sides with the melted butter and cut each slice into 3 equal rectangles.
Stand 10 of the bread rectangles inside the rim of each ramekin, overlapping them slightly. Spoon 2/3 cup of the apple mixture into each ramekin and smooth the surface. Carefully fold the bread over the filling, pressing lightly to enclose the filling. Cover the ramekins with foil and bake for 1 hour, or until the bread is slightly browned and the filling is bubbling. Remove the foil and bake for 10 minutes longer, or until the bread is browned and crisp.
Slip on an oven mitt and unmold the charlottes 1 at a time by turning them onto the mitt and then setting them right side up on dessert plates. Let cool for 15 minutes. Set a scoop of ice cream on top and serve right away.