Preheat the oven to 350°F (175°C).

Prepare the baking pan: Line the bottom with a parchment round and grease only the parchment, not the sides.

Crack the eggs into a clean stand mixer bowl.

Add all the sugar and start whisking on low speed to begin dissolving the sugar.

Once slightly dissolved, increase to high speed and whisk with a balloon whisk attachment until the mixture triples or quadruples in volume.

Add the vanilla paste and mix just to combine.

Sift the flour and cornstarch together, then add them in two additions, folding gently with a rubber spatula after each.

Fold just until no flour streaks remain, taking care not to deflate the batter.

Pour the batter into the prepared pan and bake immediately on the center rack.

Cool the cake in the pan, then loosen the sides with a knife before removing.

In a saucepan, bring the milk to a boil over medium heat.

In a bowl, whisk the yolks with sugar and cornstarch until smooth.

Temper the egg mixture by whisking in a small amount of the hot milk.

Slowly pour in the rest of the milk, whisking constantly.

Return to the saucepan and cook over medium-low heat, stirring constantly until thickened.

Remove from heat, stir in vanilla, and cool in a cold water bath, stirring occasionally.

Add the cooled custard spoon by spoon, beating well after each addition, until smooth.

Wash and slice the strawberries, reserving some whole for decoration. Set aside some buttercream for finishing.

With a paring knife, make a vertical cut 1/2 inch from the rim, about 3/4 deep.

Cut and scoop a cavity from the cake, leaving about 1/2 inch thickness around the bottom and sides.

Spread a layer of buttercream inside the cavity.

Add 1/3 of the strawberries, then top with some of the reserved cake crumbs.

Repeat with another layer of buttercream, strawberries, and crumbs.

Once filled, cover the entire cake with the reserved buttercream.

Decorate with whole and sliced strawberries.

Refrigerate for at least 3 hours before serving to let the cake set beautifully.