8 large Granny Smith apples—peeled, cored and thinly sliced (12 cups)
1/2 cup granulated sugar
1/4 cup packed dark brown sugar
1 quart chilled heavy cream
Preheat the oven to 350°. Butter and flour a 12-by-17-inch rimmed baking sheet. In a medium bowl, whisk the flour with the baking soda, salt, cinnamon, cloves and allspice. In a large bowl, using an electric mixer, beat the softened butter with the brown sugar and molasses at medium speed until combined. Add the egg and beat until blended, then add the dry ingredients in 3 batches, alternating with the buttermilk. Scrape the batter onto the prepared baking sheet and smooth the surface.
Bake the cake in the center of the oven for about 20 minutes, or until springy. Let cool in the pan for 10 minutes, then invert onto a wire rack and let cool completely.
In a medium saucepan, combine the sugar and water and cook over moderately high heat, stirring, until the sugar dissolves. Cook without stirring until a deep amber caramel forms, 5 to 6 minutes. Remove from the heat and carefully add the cream. Once the bubbling subsides, return the caramel to moderate heat and cook, stirring occasionally, until the sauce is slightly thickened, 5 to 6 minutes. Whisk in the cinnamon. Transfer the caramel to a heatproof pitcher.
In a large skillet, melt 4 tablespoons of the butter. Add half of the apples and cook over high heat, tossing occasionally, until lightly browned, about 4 minutes. Add half each of the granulated and brown sugars and cook, stirring occasionally, until the apples are caramelized and very tender, about 6 minutes. Transfer the apples to a plate, rinse out the pan and repeat with the remaining butter, apples and granulated and brown sugars.
In a large bowl, using an electric mixer, beat the cream until medium soft peaks form. Using a 2 1/2-inch biscuit cutter, stamp out 24 rounds of the cake. Spoon 1 tablespoon of caramel sauce into each of 12 large glasses. Add about 2 tablespoons of apples and 1/4 cup of whipped cream to each glass. Place a cake round in each glass. Repeat with the remaining ingredients, ending with whipped cream. Refrigerate for at least 30 minutes or overnight. Let stand at room temperature for 15 minutes; serve.
The parfaits can be assembled early in the day and refrigerated. Let stand at room temperature for 15 minutes before serving.