Peel, quarter and core the pears. Transfer to a large, heavy skillet and pour in the fruit juice. Bring to a simmer over medium-high heat; partially cover and cook until the pears are tender, about 25 minutes. Using a slotted spoon, transfer the pears to a plate. Bring the juices to a boil and cook, uncovered, until reduced to 2/3 cup, about 7 minutes. Let cool. [Make ahead: Cover the pears and syrup separately and refrigerate for up to 2 days.]
Preheat the oven to 350 degrees. Grease a 10-by-15-inch jellyroll pan. Line the pan with parchment, then grease the parchment. In a medium bowl, whisk together the flour, apple pie spice, cocoa and salt. Using an electric mixer fitted with the whisk attachment, beat the egg yolks, 2/3 cup confectioners' sugar and 1 tsp. vanilla at high speed until thick enough to hold a ribbon when the beater is lifted, 2 to 3 minutes. Sprinkle the flour mixture on top and mix at low speed until just blended.
In a clean, dry mixer bowl with a clean, dry whisk attachment, beat the egg whites and remaining 1/3 cup confectioners' sugar at high speed until stiff peaks form, about 3 minutes. Gently fold half of the whipped whites into the batter until almost incorporated. Fold in the remaining whites and fully combine. Spread the batter evenly into the prepared pan, making sure it fills the corners. Bake until springy to the touch, about 20 minutes.
Run a small, sharp knife around the edges of the hot cake to loosen from the pan. Dust the cake with confectioners' sugar. Lay a clean kitchen towel over the cake, top with a rack and invert the cake (the towel will be between the rack and the cake). Remove the pan. Loosen the parchment but leave it on top; let cool completely. [Make ahead: Wrap the cake in plastic wrap and keep at room temperature for up to 3 days.]
In a clean, dry mixer bowl fitted with a clean, dry whisk attachment, mix the mascarpone and remaining 1 tsp. vanilla at medium-high speed. Gradually pour in the cream and beat until the mixture is thick and billowy, 1 to 2 minutes; refrigerate until ready to use.
Remove the parchment and spread the dulce de leche on the cake. Cut the cake into 1-inch pieces.
Place one-third of the cake pieces in a single layer in the bottom of a trifle dish. Spoon half of the whipped cream on top, using the back of a spoon to help spread into an even layer. Starting from the edge of the dish, arrange half of the pear pieces on top of the cream. Drizzle 2 tbsp. of the pear syrup over the pears. Scatter half of the remaining cake pieces on top; drizzle with 6 tbsp. of the pear syrup. Top with the remaining whipped cream, smoothing into an even layer. Arrange the remaining pear pieces on top of the cream; drizzle with any remaining pear juices and pear syrup. Finish with the remaining cake pieces.