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Export 14 ingredients for grocery delivery
Make the pastry cream: In a medium saucepan, combine the milk, ¼ cup of the sugar, cinnamon stick and lemon zest. Warm gently over medium-low heat until the milk is barely simmering. Remove from the heat and cover with plastic wrap. Let steep until cooled to room temperature. Strain, discarding the solids and return to the saucepan. Bring to a simmer over medium heat.
Meanwhile, in a medium bowl, whisk together the egg yolks with the remaining ¼ cup of sugar, the cornstarch and salt. Whisk ½ cup of the hot milk mixture into the egg mixture to temper the eggs, then add to the pan with the remaining hot milk. Cook, whisking constantly, until the mixture is thick and creamy, 5 to 7 minutes. Strain into a bowl, then cover with plastic wrap, so that the plastic touches the surface of the custard. Let cool completely.
Make the cake: In a stand mixer bowl fitted with the paddle attachment, cream the eggs and sugar on medium speed until pale, light and fluffy, 3 to 4 minutes. Add the butter, lemon zest, salt, almond and vanilla extracts, and baking powder, and mix until just combined. Using a rubber spatula, add the flour in 3 equal additions, scraping the sides of the bowl after each addition. Divide the batter evenly between 2 pastry bags fitted with a ½-inch plain tip.
Assemble the cake: In a small saucepan, bring the water and cognac to a boil. Pour over the dried cherries and let cool. Drain the plumped cherries, discarding the liquid. Preheat the oven to 350° and grease a 9-inch springform pan with butter. Using one bag of the cake dough, pipe a thin layer of batter onto the pan, starting from the center and working outward to make a snail-shell spiral, ¼ inch thick. Using a small offset spatula, smooth out the batter on the bottom of the pan, making sure the thickness is uniform.
Scrape the pastry cream into the center and spread to evenly cover all but the outer 1-inch border of the dough. Scatter the cherries over top of the pastry cream. Repeat the piping and smoothing process with the other bag of dough, sealing in the pastry cream and cherries. Refrigerate for 1 hour. Brush the top with the beaten egg and, using a paring knife, make a series of angled scores on the top in a decorative pattern.
Bake until golden brown, 40 minutes. Let cool completely, then slice and serve.