Preheat your oven to 350°F (175°C) and prepare a 9x13-inch baking pan by greasing it or lining it with parchment paper.

Cream together ½ cup of unsalted butter and 1 cup of granulated sugar until light and fluffy. Add ½ cup of oil, 3 eggs, ½ cup of Greek yogurt, and 2 teaspoons of vanilla extract. Mix until smooth.

Sift together 2 cups of all-purpose flour, 2 teaspoons of baking powder, and ½ teaspoon of baking soda in a separate bowl. Gradually fold into wet ingredients until fully incorporated.

Pour the batter into the prepared pan and bake for about 35 minutes, until a toothpick comes out clean.

While the cake bakes, prepare the pastry cream by whisking together ½ cup of sugar and 4 egg yolks. Slowly whisk in ¼ cup of cornstarch, ¼ cup of flour, and 2 cups of simmering whole milk. Cook until thickened.

Poke holes in the cooled cake with a wooden spoon handle and pour warm pastry cream over it.

Whip 1 cup of heavy cream until soft peaks form, then fold into the cooled pastry cream.

Spread the diplomat cream over the filled cake, cover, and chill in the refrigerator for at least 2 hours.

For the ganache, heat ½ cup of heavy cream and pour over 4 ounces of chocolate. Stir until smooth.

Pour ganache over the chilled cake and refrigerate for another 2 hours before serving.