Start with the apple filling. Put the diced apples, butter, brown sugar, cinnamon, nutmeg, allspice, cloves, and boiled cider into a medium saucepan. Set it over medium high heat and cook, stirring often, for 8 to 12 minutes, until the apples are as tender as you like. In a small dish, whisk the cornstarch into the water until it dissolves, then stir it into the hot apples. Keep cooking for about 1 minute so the juices thicken. Pull the pan off the heat and chill the filling in the refrigerator to cool.

Get ready to bake. Heat the oven to 350 degrees F and line two cupcake pans with paper liners, enough for 16 to 17 cupcakes.

Begin the batter. In a medium mixing bowl, whisk together the cake flour, granulated sugar, brown sugar, baking powder, cinnamon, and salt. Add the softened butter and the oil, then beat on low speed for 30 to 60 seconds, just until the butter starts blending in and the mixture looks sandy, with a few larger butter chunks still coated in flour.

Finish the batter. In a 2 cup glass measuring cup, whisk the sour cream, milk, warm water, and vinegar until smooth. Spoon 2 tablespoons of this into the flour mixture and mix on low just until it starts coming together and no dry bits remain, but it is still lumpy. Add the vanilla and the eggs to the remaining liquid, lightly beating the eggs with a fork to break them up. With the mixer running on low, pour in half of the liquid mixture. Once it is nearly absorbed, pour in the rest and mix on low only until combined. Scrape down the bowl to catch anything stuck to the sides. A few small lumps are fine, so do not overmix.

Bake the cupcakes. Divide the batter evenly among the liners, filling each about two thirds full (roughly 52 grams per cupcake if you weigh them). Bake for 14 to 17 minutes, until a toothpick inserted in the center comes out with moist crumbs instead of wet batter. Right away, run a butter knife around the edges and lift the cupcakes out of the hot pan onto a wire rack to cool completely.

Make the frosting while the cupcakes cool. In a medium bowl, beat the butter for 30 to 60 seconds until creamy. Add the powdered sugar and mix until smooth, using the heavy cream as needed to keep things moving. Beat in the boiled cider, vanilla bean paste, salt, and cinnamon, tasting and adjusting as you go. If the frosting turns out too soft or looks weepy, chill the bowl for a few minutes until it stiffens back up.

Decorate. Confirm the cupcakes are completely cool. Use a cupcake corer or a small spoon to hollow out the center of each one, then spoon in 1 to 2 teaspoons of apple filling. Fit a piping bag with an Ateco 1A tip and pipe swirls of frosting over the tops. Drag the back of an offset spatula or spoon through the center of the frosting to create a small swirl, then add another spoonful of apple filling on top and drizzle with some of the syrupy juices from the filling.

Serve and store. These are at their best right after they are frosted. Keep any extras in an airtight container in the refrigerator for 2 to 3 days. Let chilled cupcakes sit on the counter to come back to room temperature before eating, or enjoy them cold if you prefer a denser texture.

To freeze, skip the filling and frosting. The plain cupcakes freeze well. Let them thaw on the counter for 1 to 2 hours before filling and frosting them.