Make the dough: In a large bowl, using an electric mixer, cream the butter and sugar on medium speed until light and fluffy. Beat in the egg yolk until incorporated. On low speed, mix in the flour until the dough just comes together. Turn out on a lightly floured surface and knead 3 or 4 times to form a smooth ball. Pat the dough into a 6-inch disk. Press the dough evenly into the bottom and up the sides of an 11-inch by 1-inch fluted tart pan with a removable bottom. Prick all over with a fork. Refrigerate for 1 hour.
Preheat the oven to 375 degrees. Place the tart shell on a baking sheet and bake for 10-15 minutes, until just starting to color. Set aside.
Make the filling: Peel, quarter and core the apples; slice lengthwise 1/4 inch thick. In a bowl, toss the apples and cranberries with the flour. Sir in the sugar and cinnamon. Mound the filling in the tart shell.
Make the topping: In a medium bowl, combine the oats, flour and brown sugar. Pour in the butter and crumble the mixture with your fingers. Pile it on the fruit to cover completely.
Bake the tart for about 40 minutes, or until the topping is golden, the filling is bubbling and the apples are tender when pierced. (Cover loosely with foil if the top gets too brown too soon). Transfer to a rack to cool. Prep time includes refrigeration time for crust.