Preheat the oven to 375 degrees F.

Peel, core, and slice apples into 1/4-inch slices. Cover the bottom of a 9-inch deep-dish pie plate with the apple slices and sprinkle with the raisins.

In the bowl of an electric mixer fitted with the paddle attachment, beat 3/4 cup of the sugar and the butter on medium speed for 4 to 5 minutes, or until light and fluffy. Add the egg and then 1 1/2 cups flour and mix well.

Sprinkle a work surface with about 1/4 cup flour. Turn the dough out onto the work surface and work it by hand as you flatten it into a crust that is 1/4 to 1/2 inch thick. (You could also roll the dough with a rolling pin.) Pat the dough lightly to flatten it. Cut the crust into 2-inch squares and lay these over the apples to create a patchwork effect. Brush with the cream.

In a small bowl, stir together the remaining tablespoon of sugar, the cinnamon, and the walnuts, if using. Sprinkle over the crust and bake for 15 minutes. Lower the oven temperature to 350 degrees F. and bake for 30 to 35 minutes longer, or until the crust is golden brown and the apples are bubbly. Serve warm or at room temperature.