Step 1: Preheat oven to 350°F (175°C). Grease and flour two 8-inch round cake pans. Line bottoms with parchment paper.
Step 2: In a medium bowl, whisk together the sifted cake flour, baking powder, and salt. Set aside.
Step 3: In a large bowl, cream softened butter and 1 cup granulated sugar until light and fluffy. Beat in eggs one at a time, then stir in vanilla extract.
Step 4: Gradually add the dry ingredients to the wet ingredients, alternating with the ½ cup whole milk, beginning and ending with the dry ingredients. Mix until just combined. Do not overmix.
Step 5: Divide batter evenly between the two prepared cake pans. Bake for 25-30 minutes, or until a wooden skewer inserted into the center comes out clean. Let cool in pans for 10 minutes, then invert onto a wire rack to cool completely.
Step 6: While cakes cool, prepare the custard. In a medium saucepan, heat 1 ½ cups whole milk over medium heat until simmering. In a separate bowl, whisk together remaining ½ cup whole milk, ½ cup granulated sugar, cornstarch, and egg yolks until smooth.
Step 7: Slowly temper the egg yolk mixture by whisking a small amount of the hot milk into the egg mixture, then gradually pour the egg mixture back into the saucepan with the remaining hot milk, whisking constantly.
Step 8: Cook over medium-low heat, whisking continuously, until the custard thickens significantly and coats the back of a spoon (about 5-7 minutes). Remove from heat, stir in 2 tablespoons unsalted butter and 1 teaspoon vanilla extract.
Step 9: Pour custard into a clean bowl, cover the surface directly with plastic wrap to prevent a skin from forming, and chill in the refrigerator for at least 2 hours, or until completely cold and firm.
Step 10: Once cakes and custard are chilled, begin assembly. If strawberries are tart, gently toss sliced strawberries with ¼ cup sugar and let sit for 15 minutes. Drain any excess liquid.
Step 11: Place one cake layer on your serving platter. Spread half of the chilled custard evenly over the cake layer. Arrange half of the sliced strawberries over the custard.
Step 12: Carefully place the second cake layer on top. Spread the remaining custard, then top with the rest of the fresh sliced strawberries. Chill the cake for at least 30 minutes before serving for best results.