For the spiced strawberries: Set 1 cup of whole strawberries aside (pick the ones that are similar in size--they will be used to decorate the cake). Hull and halve the remaining strawberries. Place 2/3 cup water, the sugar, black pepper and salt in a medium saucepan and bring to a boil over high heat. Reduce the heat to medium and stir until the sugar has completely dissolved. Turn off the heat and add the halved strawberries, stirring to coat them with the syrup. Cool the strawberries in the syrup to room temperature, then refrigerate the strawberries and syrup until completely chilled (the strawberries can be made up to 1 day in advance).
For the sponge cake: Use the room temperature butter to lightly grease an 8-inch cake pan; line it with an 8-inch parchment paper circle and lightly grease the paper circle. Preheat the oven to 320 degrees F for a convection oven or 350 degrees F for a regular oven.
Sift the flour and baking powder together into a medium bowl, then add the salt and set aside.
Using a stand mixer fitted with the whisk attachment or a large bowl and a hand mixer, beat the eggs with the sugar until thick, pale and fluffy, about 5 minutes. Pour in the melted butter and yogurt and beat to combine. Fold the flour mixture into the egg mixture by hand, gently folding the ingredients together until no streaks of flour remain (take care not to over-mix or the cake will be heavy).
Scrape the batter into the prepared cake pan and bake until a cake tester comes out clean, 45 to 50 minutes. If the cake is browning too fast, loosely cover the top with aluminum foil. Remove the cake from the oven, let it rest for 5 minutes and then invert the cake onto a wire rack to let it cool completely, at least 30 minutes. (Once cool, the cake can be wrapped in plastic wrap and held at room temperature for 1 day before dividing into layers.)
For the vanilla cream: Add the cream to the bowl of a stand mixer fitted with the whisk attachment or to a medium bowl if using a hand mixer. Use a paring knife to make a long incision along the length of the vanilla pod. Open the pod and use the back of the knife to scrape out the seeds, adding them to the cream (discard the pod). Add the sugar to the cream and whip until it holds stiff peaks.
To assemble: Pour the spiced strawberries into a fine-mesh sieve set over a medium bowl and let them drain thoroughly.
Divide the cake horizontally into 3 even layers (see Cook's Note). Set the top layer of cake on a cake plate or large plate. (Save the bottom of the cake with the flat surface that touched the bottom of the cake pan for the top cake layer, so the top of the cake has a nice, smooth and flat surface to frost.) Use a pastry brush to dab the top side of the cake layer generously with the strawberry syrup.
Spread a quarter of the vanilla cream on top of the cake layer and use a slotted spoon to add a third of the drained strawberries, arranging them into an even layer. Repeat twice more. Spread or pipe the rest of the cream around the sides and top of the cake (dip an icing spatula into hot water before frosting the top and sides of the cake for the smoothest finish). Top the cake with the remaining fresh strawberries and serve immediately or refrigerate for up to 2 days before serving.
For even layers, place the whole cake upside-down on a plate with a raised edge and use the edge of the plate to guide the bread knife across the bottom of the cake in a straight line. Gently remove the top portion of the cake (you can discard the rounded top you just sliced off). Repeat this process to end up with 3 even layers of cake.
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