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Step 1
Coat an 8- or 9-inch round cake pan and a large bowl with cooking spray. Line the bottom of the cake pan with a parchment paper round.
Step 2
Dice 4 tablespoons unsalted butter. Place the butter and 1/4 cup whole milk in a small saucepan. Heat over medium-low heat until the butter is almost melted and the milk is hot to the touch (about 110ºF); swirl the pan to fully melt the butter. Transfer to the bowl of a stand mixer.
Step 3
Lightly beat 2 large eggs in a small bowl until broken up. Add the eggs, 1 cup all-purpose flour, 1 cup bread flour, 1/4 cup granulated sugar, 1 (1/4-ounce) packet instant yeast, and 1/2 teaspoon kosher salt to the milk mixture. Stir with a wooden spoon until a sticky dough forms.
Step 4
Fit the bowl onto the stand mixer. Mix with the hook attachment on medium speed until a smooth but still-sticky dough forms, 5 to 7 minutes. Scrape the dough into the oiled bowl. Cover the bowl with plastic wrap and let the dough rise in a warm place until puffy but not quite doubled in size, about 1 hour. Meanwhile, wash and dry the stand mixer bowl. Make the pastry cream.
Step 5
Fit a fine-mesh strainer over a medium bowl. Place 3/4 cup of the whole milk, 2 tablespoons of the granulated sugar, 1 teaspoon vanilla bean paste, and 1 pinch kosher in a medium saucepan. Whisk to combine and place over medium-low heat.
Step 6
While the milk mixture is heating, roll up a kitchen towel lengthwise, then make the ends meet to form a circle. Place the remaining 1/4 cup whole milk, remaining 2 tablespoons granulated sugar, and 2 tablespoons cornstarch in a second medium bowl. Whisk until smooth. Add 2 large egg yolks and whisk until lightened in color. Place this bowl in the center of the towel circle.
Step 7
Once the milk mixture on the stove comes to a simmer, pour half of it into the egg yolk mixture in a steady stream while whisking constantly (the towel should hold the bowl steady while you whisk). While whisking constantly, pour the yolk mixture back into the saucepan. While whisking constantly, bring back to a simmer and cook until thickened, about 5 minutes.
Step 8
Turn off the heat. Add 1 tablespoon unsalted butter and whisk until the butter is melted and the mixture is smooth. Scrape into the fine-mesh strainer and press the mixture through with a flexible spatula, making sure to scrape the underside of the strainer; discard the contents of the strainer.
Step 9
Press a sheet of plastic wrap directly onto the surface of the pastry cream to prevent a skin from forming. Refrigerate until cold, about 1 hour and 15 minutes. Meanwhile, bake the cake.
Step 10
Lightly dust a work surface with all-purpose flour. Transfer the dough onto the work surface. Degas the dough by pressing down to release any large air bubbles. Loosely shape into a ball and place in the cake pan. Press the dough evenly in the pan, going all the way to the edges (if it springs back, let rest for 5 minutes before trying again).
Step 11
Cover with plastic wrap and let rise in a warm spot until slightly puffed, about 30 minutes. Meanwhile, arrange a rack in the middle of the oven and heat the oven to 350ºF.
Step 12
Make the topping when the dough is ready. Place 4 tablespoons unsalted butter, 3 tablespoons honey, 3 tablespoons granulated sugar, 1/2 teaspoon vanilla bean paste, and 1 pinch kosher salt in a small saucepan. Stir to combine and bring to a simmer over medium heat. Add 1 cup sliced almonds and stir to combine.
Step 13
Dollop the mixture over the dough and spread into an even layer. Place the cake pan on a baking sheet. Bake until puffed and golden-brown, 30 to 32 minutes. Immediately run a thin knife around the cake to keep the topping from sticking. Let cool for 20 minutes in the pan.
Step 14
Flip the cake out of the pan, remove the parchment, and place the cake right-side up on a wire cooling rack. Let cool completely, about 1 hour more.
Step 15
Place 4 teaspoons water in a small microwave-safe bowl and sprinkle 3/4 teaspoon powdered unflavored gelatin over the water. Let sit for 5 to 10 minutes. Meanwhile, place the pastry cream in the stand mixer bowl and beat with the paddle attachment on medium speed until smooth and spreadable, about 2 minutes. Return the pastry cream to the bowl it was chilled in.
Step 16
Microwave the gelatin mixture until melted, about 10 seconds. Place 3/4 cup cold heavy cream and 3 tablespoons powdered sugar in the stand mixer (no need to clean first). Fit with the whisk attachment and turn on to low speed. Slowly add the melted gelatin. Once incorporated, increase the speed to medium-high and whip until stiff peaks form, about 2 minutes.
Step 17
Transfer about 1/3 of the whipped cream into the pastry cream and stir with a flexible spatula until smooth. Add the remaining whipped cream and gently fold until just combined.
Step 18
Slice the cake in half horizontally. Place the bottom half of the cake cut-side up on a cake stand or serving plate. Transfer the filling onto the cake and spread into an even layer, going all the way to the edges. Let sit for 2 minutes. Top with the top half of the cake cut-side down. Refrigerate until the filling is set, about 1 hour.