Preheat the oven to 350F (180C), and line an 8-inch pan with parchment paper.
Sift the two types of flour into a bowl and mix in the baking powder.
Mix the milk and vanilla extract in a saparate measuring cup and mix.
In a bowl of a stand mixer, beat the butter, sugar, and vanilla paste for 4-5 minutes until light and fluffy.
Add the eggs, one at a time, waiting for the first egg to completely incorporate before adding the second. Use a rubber spatula to scrape the bottom and sides of the bowl.
Reduce the speed to low, and add 1/3 of the flour mixture to the egg-butter mixture, followed by the milk mixture.
Incorporate the rest of the flour into the mixture, using a rubber spatula.
Spread the cake batter into the prepared pan, and dot the top with the pastry cream.
Bake for 38-44 minutes, or until a toothpick comes out with a few moist crumbs from the center of the cake.