Make the dough: Combine the flour, cornstarch, sugar, and salt in the bowl of a stand mixer fitted with the paddle attachment. Turn the machine on to low and beat for 10 to 15 seconds to mix them together. Add the butter and shortening and beat on medium-low speed for about 3 minutes, until the dough looks like clumpy sand-it should still be shy of the gravelly/pellet stage.

Add the vinegar to the water and then, with the mixer running on medium-low speed, add the liquid to the coalescing dough a few tablespoons at a time: this dough will be much wetter and more overworked than you'd ever want a traditional pie or tart dough to be. It should take about 2 minutes of mixing for it to come together into a dough; mix it for a couple of additional minutes once it does. Take the gummy dough out of the mixer, shape it into a flat, thick square or rectangle, wrap it in plastic, and refrigerate it for at least an hour. Freeze apple pie dough for up to 2 weeks if you are not going to use it the day you make it. Defrost in the refrigerator before proceeding.

Bring the dough back up to almost room temperature; it will be shiny and greasy, not a pretty pastry dough. Tosi uses a scale to measure the amount of dough she needs for forming the pies and you should too. You need 6 tops and 6 bottoms. For the bottoms, grab off 50-gram (golf ball-sized) pieces of dough and on a lightly floured surface roll into rectangles that measure 6 by 3½ inches; for the tops, roll out 30-gram (Ping Pong ball-sized) nuggets of dough into rectangles that measure 5 ½ by 4 inches. Both should be just more than an ⅛ inch thick.

Generously flour the molds. Press each of the larger bottom rectangles into a 4½ by 2½ by ¼-inch mold (failing a rectangular mold, you could substitute fluted mini-tart pans with removable bottoms, in which case, you'd need to roll the dough out into circles to fit your pans), making sure the dough is flush against the fluted sides and the bottom, with a very slight excess of dough hanging over the edges. Put ⅓ cup (75 grams) apple filling in each one, and use the back of a spoon to smooth it out. Tap each mold against the counter to make sure the apples shimmy their jellied selves into the corners of the mold; there should be some clearance between the top of the apple mush and the rim of each mold. Dip a pastry brush in a bowl of cold water and moisten the edges of the dough in the molds, then gently lay the other rectangles of dough over the molds, crimping the tops and bottoms of the dough together all the way around.

Freeze the pies in the molds for 30 minutes, just enough time for the dough to firm up and release itself from the mold. Pop the pies out of the molds, transfer them to a rimmed baking sheet, wrap it in plastic, and freeze the pies until frozen solid, at least a few hours. You can keep the pies frozen for weeks before proceeding.

When you're ready to serve the dessert, heat a quart or two of oil to between 350° and 370°F in a large pot with high sides. Set up a cooling rack for the pies to drain on after they're fried. Put the cinnamon dust in a small sieve to use to dust the pies with later, and set it on a plate. Turn the oven to 250°F-it doesn't need to preheat; it just needs to be warm. Set a cooling rack over a baking sheet and put it in the oven, to keep the just-fried pies hot until ready to serve.

When the oil reaches temperature, use a slotted spoon to lower a frozen pie into the hot oil (frying them one at a time is the most advisable course of action). The oil will bubble and hiss a bit when the pie goes in, but the bubbling should subside as it sinks to the bottom of the pot. After a couple of minutes, the pie will become more buoyant, and in 4 to 6 minutes, it should be taking on a good auburn color-getting a good brown on the pie makes it more delicious and is a good visual indication that the inside will be appropriately piping hot. When it's browned and bobbing up near the surface of the oil, scoop it out of the pot and transfer it to the cooling rack to drain (actually, for the first 4 pies, transfer to the rack in the oven to drain and stay hot). After a minute or so, once the pie has shaken off the searing heat of the fryer, dust the top of it generously with cinnamon dust. Fry the rest of the pies. (Don't worry if a pie leaks or develops a crack-we wouldn't serve a pie like that at Ko, but we've eaten a few of those rejects, and they just have an extra deep-fried flavor to them.)

To plate the apple pies, plop down a very generous tablespoon of miso butterscotch slightly off the center of each of six wide white plates. Use the back of the spoon to schmear the butterscotch across the plate. Arrange a fried pie on the plate perpendicular to the butterscotch schmear. Scoop out a quenelle or ball of sour cream ice cream and arrange it on the plate. Serve at once.