Mix the apples with ¼ cup sugar and the cinnamon. Mash the breadcrumbs, 2 or 3 tablespoons sugar, and ½ cup softened butter together with a fork. Melt the remaining ¼ cup butter in a small heavy frying pan and pack the breadcrumb mixture against the bottom and sides with a fork to form an even shell. Fill with the apple mixture, packing with the fork, and cook over a low flame, covered, for about 15 minutes or until the edges of the breadcrumb casing begin to show brown. Finish, uncovered, in the oven (375) another 15 minutes. If the contents of the pan do not slide freely with gentle shaking, loosen the bottom with a spatula before unmolding.