Creme Brûlée Cake

In a medium saucepan, heat the milk over medium-low heat just until it’s steaming. Then, turn heat down to low until ready to use.
2 1/4 cups (540 ml) whole milk
To a large bowl add the egg yolks, sugar, salt, vanilla, and cornstarch and whisk until combined and a pale-yellow color. (It will be thick at first but will get smooth as you whisk.)
6 egg yolks, 1 cup + 2 tbsp (225 g) granulated white sugar, 1/8 tsp salt, 1 1/2 tbsp vanilla bean paste, 3 1/2 tbsp (28 g) cornstarch
Add in 1/4 of the heated milk while stirring vigorously. Then, add the rest in and stir to combine.
Transfer the mixture to the saucepan. Heat over medium-low heat and cook for 12-15 minutes, whisking continuously, until the mixture is thick and soft peaks form.
Remove the pastry cream from the heat and transfer it to a bowl. Add in the butter and mix to combine. Place plastic wrap right on top of the pastry cream to prevent a skin from forming. Chill it in the fridge until completely cold.
3 tbsp (42 g) unsalted butter, cold and cut in cubes

Preheat the oven to 350℉ (175 ℃). Grease a 9×9in pan and line it with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Then set aside the flour mixture.
2 1/4 cups (281 g) all-purpose flour, spooned and leveled, 1 1/2 tsp baking powder, 1/4 tsp baking soda, 1/2 tsp salt
Add the softened butter and granulated white sugar to a large bowl. Cream together for 2 minutes with an electric mixer.
(You can also use the bowl of a stand mixer fit with a paddle attachment.)
10 tbsp (140 g) unsalted butter, softened, 1 1/2 cups (300 g) granulated white sugar
Then add in the eggs and vanilla and mix on medium speed until pale in color and smooth, about 1 minute.
3 large eggs, at room temperature, 1 1/2 tbsp vanilla bean paste
Add the dry ingredients and buttermilk to the wet ingredients a little at a time, mixing on low speed until the cake batter is combined. Scrape the sides of the bowl with a rubber spatula as necessary.
1 cup (240 ml) buttermilk, at room temperature
Pour the batter into the prepared pan. Bake the cake for 39-44 minutes or until a toothpick comes out clean from the center.
Let the cake cool in the pan on a wire rack for 30 minutes. Carefully pull up on the parchment paper to release the cake from the pan, then continue to cool it on the wire rack until completely cooled.

In a liquid measuring cup, whisk the half & half, sweetened condensed milk and vanilla together. Chill in the fridge until ready to use.
1/2 cup (120 ml) half & half, or whole milk, 1/2 cup (120 ml/150 g) sweetened condensed milk, 1 1/2 tsp vanilla bean paste

When the cake is completely cooled, cut a very thin layer off the top of the cake off using a sharp knife. This will make it easier for the vanilla milk to absorb into the cake. Transfer it to a serving plate. Poke holes on the top of the cake using a wooden stick or the handle of a wooden spoon.
Slowly pour the vanilla milk mixture on top of the cake. It is thin so it should absorb into the cake and the poked holes easily, but do be patient as it does.
Spoon the chilled vanilla pastry cream on top of the cake. Use an offset spatula to smooth it out.
Cut the cake into 16 squares.
Sprinkle sugar over each piece of cake. Use a kitchen torch to brûlée the sugar until it is golden brown and smells like roasted marshmallows. Then, enjoy! :)
(Add the pastry cream on top of the cake right before you're ready to serve it. After a few hours the brûlée topping will start to melt, so you'll want to enjoy the cake right away.)
1/3-1/2 cup (66-100 g) granulated white sugar (for the brûlée topping)