Step 1: Make the Pastry Cream

1. Heat the Milk and Cream: In a saucepan, whisk together the whole milk, heavy cream, 1/4 cup of the granulated sugar, and the salt. Place the saucepan over medium heat and stir frequently until the mixture begins to steam and the sugar dissolves. Remove the saucepan from the heat and let it cool for about 10 minutes.
2. Prepare the Egg Mixture: While the milk and cream mixture cools, whisk the egg yolks and the remaining 1/4 cup of sugar in a separate bowl. Beat until smooth and creamy. Add the cornstarch and continue whisking until the mixture is free from lumps.
3. Temper the Eggs: Gradually add about 1/3 of the hot milk mixture to the egg yolk mixture, whisking constantly to prevent the eggs from curdling. Once combined, slowly whisk the egg mixture back into the saucepan with the remaining milk mixture.
4. Cook the Pastry Cream: Return the saucepan to medium heat and cook the mixture, whisking constantly, for 2-3 minutes until it thickens to a pudding-like consistency. This step is important—make sure the pastry cream reaches the right thickness before moving on.
5. Strain and Finish: Strain the pastry cream through a fine-mesh sieve into a bowl to remove any lumps or bits of egg. Add the vanilla extract and softened butter, whisking until fully incorporated.
6. Chill the Pastry Cream: Press plastic wrap directly onto the surface of the pastry cream to prevent a skin from forming. Refrigerate for at least 2 hours or until the cream is fully chilled.

Step 2: Make the Cupcakes

1. Preheat the Oven: Set your oven to 350°F (175°C) and line two 12-count muffin pans with cupcake liners.
2. Cream the Butter and Sugar: In a large bowl, beat the softened butter, vegetable oil, and granulated sugar together until the mixture is light and fluffy, about 2 minutes. This step is key to achieving soft, tender cupcakes.
3. Add the Eggs and Vanilla: Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract until the mixture is smooth and fully combined.
4. Combine the Dry Ingredients: In a separate bowl, whisk together the all-purpose flour, baking powder, and salt. Gradually add the dry ingredients to the butter mixture, alternating with the buttermilk. Add the dry ingredients in three additions, starting and ending with the dry ingredients. Mix until just combined to avoid overmixing.
5. Fill the Cupcake Liners: Divide the cupcake batter evenly between the cupcake liners, filling each about 3/4 of the way full.
6. Bake the Cupcakes: Bake for 18-20 minutes, or until a toothpick inserted into the center of the cupcakes comes out clean or with just a few moist crumbs. Allow the cupcakes to cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.

Step 3: Make the Ganache Topping

1. Combine Ingredients: In a microwave-safe bowl, place the semisweet chocolate chips, heavy cream, and corn syrup (if using). Microwave the mixture in 20-second intervals, stirring well between each, until the chocolate is fully melted and smooth.
2. Add the Sugar: Sift in the confectioners’ sugar and whisk until fully incorporated. The ganache should be smooth and glossy.
3. Cool the Ganache: Let the ganache sit for 10-15 minutes at room temperature to thicken slightly before using.

Step 4: Assemble the Cupcakes

1. Cut a Hole in the Cupcakes: Once the cupcakes have completely cooled, use a paring knife to cut a cone-shaped cavity from the center of each cupcake. Be sure to only cut about 3/4 of the way down, leaving the bottom intact.
2. Fill the Cupcakes: Transfer the chilled pastry cream to a piping bag fitted with a round tip. Pipe the cream into the cavity of each cupcake, filling it to the top.
3. Replace the Tops: Gently place the cone-shaped piece of cupcake back on top of the cream to seal it in.
4. Drizzle the Ganache: Spoon or drizzle the slightly thickened ganache over the tops of the filled cupcakes. The ganache should beautifully cover the tops and drip slightly over the edges.
5. Refrigerate the Cupcakes: Refrigerate the cupcakes until ready to serve. This will help the ganache set and make them even more delicious.