How to Make It
In a large bowl, using an electric mixer, cream the butter and sugar on medium speed until light and fluffy, about 3 minutes. Beat in the egg yolk until thoroughly incorporated. On low speed, mix in the flour until the dough just comes together. Turn out the dough 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-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°. Place the tart shell on a baking sheet and bake until just starting to color, 10 to 15 minutes. Set aside.
Using a small sharp knife, peel, quarter, and core the apples. Slice them lengthwise 1/4 inch thick. In a large bowl, toss the apples and cranberries with the flour. Stir in the sugar and cinnamon. Mound the filling in the tart shell.
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 top of the fruit filling to cover completely.
Bake the tart for about 40 minutes, or until the crumb topping is golden, the fruit filling is bubbling and the apples are tender when pierced with a cake tester. (Cover the tart loosely with a sheet of foil if the top gets too brown before the bubbling begins.) Transfer to a rack to cool.