How to Make It
Place flour, 1 1/4 teaspoons salt, and 1/2 teaspoon pepper in a food processor; pulse until combined, about 2 times. Add cubed butter, and pulse in 1-second bursts until mixture resembles coarse meal, 8 to 10 times. Drizzle 7 tablespoons ice water over flour mixture, and pulse until dough comes together, 8 to 10 times. Turn dough out onto a lightly floured work surface; gather up any crumbs, and pat into a disk. Wrap disk in plastic wrap, and refrigerate until chilled, about 45 minutes.
Preheat oven to 375°F. On a lightly floured work surface, roll out chilled dough into a 12-inch round. Fit dough round into a 10-inch fluted tart pan with removable bottom, pressing dough onto bottom and into fluted edges of pan. Trim overhang until even with rim of pan. Chill tart shell 30 minutes.
Line tart shell with parchment paper, and fill to top with pie weights or dried beans. (This ensures your dough won’t shrink down the sides when baking.) Bake in preheated oven until crust is set and light golden, about 40 minutes. Remove weights and parchment; bake until golden and crisp, 10 to 12 minutes. Let cool.
Place 1 strip of ham on a work surface. Arrange a row of slightly overlapping apple slices lengthwise on ham strip; roll up loosely, and place in baked tart shell, spiral side up. Repeat process with remaining ham strips and apple slices to fill tart shell. Sprinkle cheese over top. Whisk together half-and-half, eggs, egg yolk, thyme, remaining 1 1/2 teaspoons salt, and remaining 1/2 teaspoon pepper. Pour custard in and around apple-ham rolls.
Bake at 375°F until custard is just set, 45 to 50 minutes, loosely tenting with foil to prevent excess browning, if necessary. Transfer quiche to a rack, and let cool 15 minutes. Carefully lift quiche out of pan and cut into wedges. Serve warm or at room temperature.