Make the dough: Stir dry ingredients together in a large bowl. Add butter and cut in using a pastry blender, scraping it with a knife occasionally to free any clumps. Keep at it until you are left with pea sized bits of butter in an overall crumb-like mix. Be careful not to overwork the dough. A few larger butter clumps are okay.

Pour water and vinegar together and add an ice cube or two. Drizzle a little at a time over the flour mixture and cut in. It will appear shaggy as it absorbs the liquid and as you keep cutting it together, the dough will form. Pinch the dough with your thumb and index finger to see if it holds together. If it’s crumbly, it isn’t ready. Drizzle another tablespoon or so of the cider liquid and cut in again. Once the dough has formed, empty out into three equal portions on three pieces of cellophane.

Press opposite ends of the cellophane together to form the dough into a ball. Flatten into a disk, wrap securely, and repeat with remaining two dough piles. Refrigerate all for at least 20 minutes to let them mellow.

Make the filling: Peel, core, and cut apples into wedges. Squeeze lemon juice to coat in a large bowl, mixing the juice and apple slices together to prevent from browning. Add zest, flour, salt, sugars, nutmeg, cinnamon, and rosemary, and stir to combine. Set aside while you make the brown butter.

In a light-colored sauté pan - so you can monitor the change in color as it browns - melt butter over medium heat. Let it foam and give it a swirl every so often to ensure it is cooking evenly. The process should take about 7 minutes; pay attention to the milk solids which settle at the base of the pan as you don’t want them to burn.

Once the nutty aroma becomes apparent and the butter has turned caramelly, remove pan from heat. Pour brown butter and solids over the apple mixture and stir to combine. (If the milk solids are burnt, you may choose not to add them - once cool enough to taste, try a little bit and see if you like the flavor, and then decide.) Refrigerate the mixture at least 4 hours, up to overnight.

Roll the dough: for the bottom crust, roll out one disk of dough to about 1/8-inch thick between pieces of lightly floured parchment. Peel away one sheet of parchment, flip and drape dough into an 8-inch pie plate, then peel the second parchment layer away. Trim pastry edge flush with pie plate, save scraps to re-roll, and chill. You can do this a day in advance.

Roll out the other two disks to 1/8-inch thick using the same method with parchment. Transfer dough on parchment to rimmed baking sheets and chill in the refrigerator for at least 30 minutes, or freezer for 10.

Working one sheet of dough at a time, use a flour-dusted cookie cutter to cut shapes. Gather scraps to re-roll as needed and refrigerate cutouts on a baking sheet as you go. If at any time the shapes start to stretch or you don’t get a clean cutout, refrigerate the dough.

You’ll need at least 32 cutouts for the shingled crust, depending on the size of your cookie cutter. Keep cutouts refrigerated until time to use. This can also be done a day in advance.

Drain sugar-butter mixture from apples into a saucepan and reduce by half. Add reduced syrup back to the apple mixture and stir to combine. Reducing the liquid will create a sumptuous pie, rather than a watery one.

Preheat oven to 400°. Fill pie shell with syrupspice- apple mixture, slightly mounding the fruit at the center. Lightly brush pie edge with water. Lightly brush water on back of shapes as you layer them. Starting at outermost edge, layer dough shapes like shingles, lightly brushing their undersides, pressing gently to seal them together.

Once you have made one ring of shingles, layer a second ring in the same fashion. Continue until only a small opening remains at the top. Brush beaten egg over the surface of the dough and scatter demerara sugar to coat. Refrigerate for at least 30 minutes, up to 3 hours. The colder your pastry, the better it will hold up in the oven!

Bake on a parchment lined baking sheet for 15 minutes at 400°, just so crust begins to brown. Lower heat to 350° and continue baking until crust is golden all over and juices bubble, about 55 minutes more.

Cool completely on a wire rack and serve with creme fraiche or ice cream. Pie will keep for 2 days unrefrigerated and wrapped in foil, and up to 5 days in the refrigerator in a container with a tight-fitting lid.