Cut the crabapples in half and core them, making sure they are approximately the same size. If using a smaller variety of crabapple (less than 1-inch diameter), just cut them in half. Squeeze lemon juice over the apples as you go (to prevent browning). Add zest, salt, sugars, nutmeg, rosemary, and cinnamon, and stir to combine.

Put the butter in a saucepan and melt it over medium heat. Mix in the crabapple mixture. Cook until the apples are soft and you have a thick, syrupy sauce of caramelized butter and sugar in your pan. Let cool.

To make the dough, combine all of the dry ingredients in a large bowl. Using a pastry blender or two knives, cut in the butter until you have small pieces or clumps of butter still visible in your dough. Drizzle in your vinegar and ice water slowly, cutting into flour a little at a time. Keep adding until your dough has formed and is easily pliable. Wrap in plastic and refrigerate while you prepare your filling.

Divide the chilled dough into four portions. Lightly flour the working surface, and roll out one portion about ⅛ inch thick. Cut out circles with a biscuit cutter, a mason jar lid or the mouth of a wide glass. Transfer the dough on parchment to baking sheets and chill in the refrigerator for at least 30 minutes.

Using half your dough circles, place an even amount of apple filling in the center of each one. Leave a little bit of room around the perimeter for pinching. Cut out stars or other shape from half of the remaining circles and set them aside. Dip a pastry brush into water and brush the perimeters of your circles, then place the tops over the fruit. Seal in the fruit by pinching the edges together with a fork or your fingers. Place dough cut-outs on top of some of your pastry circles (leave a few without cut-outs). If you have no cut-out tool, you can simply cut slits in the top.

Brush a beaten egg on the tops of the dough circles and sprinkle coarse sugar over them. Bake on a parchment-lined baking sheet for 10 minutes at 400 degrees F. Lower heat to 350 degrees F and continue baking until crust is golden brown all over and juices bubble, about 30 minutes more.

Cool completely on a wire rack or serve warm with whipped cream or ice cream.