Dried-Apple Stack Cakes

Preparation

1. Make filling:

   Step 1

   Simmer all filling ingredients and a pinch of salt in a 4- to 5-quart heavy pot, uncovered, stirring occasionally and mashing apples with a potato masher as they soften, until a thick purée forms, about 1 1/2 hours. Cool completely.

2. Make cakes:

   Step 2

   Preheat oven to 350°F with rack in middle. Butter muffin cups.

   Step 3

   Stir together milk and vinegar and let stand 10 minutes to curdle.

   Step 4

   Sift together flour, baking soda, salt, ginger, and cloves.

   Step 5

   Beat butter and brown sugar with an electric mixer at medium speed until pale and fluffy, about 3 minutes. Beat in molasses and egg. At low speed, add flour mixture in 3 batches alternately with curdled milk, beginning and ending with flour mixture and mixing until each addition is just incorporated. Spread 1 heaping tablespoon batter in each muffin cup and bake just until a wooden pick inserted in center of a cake comes out clean with some crumbs adhering, 11 to 13 minutes. Cool 5 minutes in pans on racks, then invert onto racks to cool completely.

3. Assemble cakes:

   Step 6

   Spread about 2 tablespoons filling on top of 1 cake and invert another cake over filling, then spread a heaping tablespoon filling on top. Make 11 more stacks (you will have about 2 cups filling left over). Transfer to an airtight container and chill at least 2 days for flavors to develop. Bring to room temperature before serving.