In a medium saucepan, heat the milk over medium heat until it's steaming and small bubbles form around the edges. Do not let it boil.

In a separate medium bowl, whisk together the sugar, cornstarch, and salt. Whisk in the egg yolks until the mixture is pale yellow and smooth.

Slowly pour about half of the hot milk into the egg yolk mixture while whisking constantly. This is called tempering and prevents the eggs from scrambling.

Pour the tempered egg mixture back into the saucepan with the remaining milk. Cook over medium heat, whisking constantly, until the custard thickens and comes to a boil. Let it bubble for 1 minute, still whisking, then remove from the heat.

Whisk in the softened butter and vanilla extract until smooth. Strain the custard through a fine-mesh sieve into a clean bowl. Press a piece of plastic wrap directly onto the surface of the custard to prevent a skin from forming. Refrigerate for at least 4 hours, or until completely chilled and set.

Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan and line the bottom with parchment paper.

In a large bowl or the bowl of a stand mixer, beat the eggs and sugar on high speed for 5-7 minutes, until the mixture is thick, pale, and triple in volume. Beat in the vanilla extract.

In a separate bowl, whisk together the flour, baking powder, and salt.

Sift one-third of the dry ingredients over the whipped egg mixture and gently fold it in with a spatula. Repeat two more times, folding just until no flour streaks remain. Do not overmix.

In a small bowl, combine the warm milk and melted butter. Add a large scoop of the batter into the milk mixture and stir to lighten it. Gently fold the lightened milk mixture back into the main batter.

Pour the batter into your prepared pan and smooth the top. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 10 minutes before inverting it onto a wire rack to cool completely.

Once the cake is completely cool, use a long serrated knife to carefully slice it in half horizontally, creating two even layers.

Place the bottom layer of the cake on your serving platter. Retrieve your chilled custard and give it a good whisk to loosen it up. Spread the custard evenly over the bottom cake layer, leaving a small border around the edge.

Gently place the top layer of the cake over the custard.

Arrange the sliced fresh strawberries on top of the cake. You can create a pattern or a simple, rustic pile.

Refrigerate the assembled cake for at least 30 minutes to allow the custard to firm up slightly before slicing. Dust with powdered sugar just before serving, if desired.