In a saucepan, whisk together the milk, cream, 1/4 cup of the granulated sugar, and the salt. Heat over medium, stirring frequently, until steaming and sugar dissolves. Remove from heat and let cool for 10 minutes.

In a bowl, whisk together the egg yolks and remaining 1/4 cup granulated sugar until smooth. Whisk in the cornstarch until no lumps remain.

Gradually whisk 1/3 of the hot milk mixture into the egg yolk mixture to temper it. Then whisk the egg mixture back into the saucepan with the remaining milk mixture.

Return saucepan to medium heat and cook, whisking constantly, until thickened to a pudding-like consistency, about 2-3 minutes.

Strain the pastry cream through a mesh sieve into a bowl. Whisk in the vanilla and butter until fully incorporated.

Press plastic wrap directly onto the surface to prevent a skin from forming. Refrigerate until completely chilled, at least 2 hours.

Preheat oven to 350°F. Line two 12-count muffin pans with cupcake liners.

In a large bowl, beat the butter, oil and granulated sugar together until light and fluffy, about 2 minutes.

Beat in the eggs one at a time, then the vanilla, until fully incorporated.

In a separate bowl, whisk together the flour, baking powder and salt.

Alternate adding the dry ingredients and buttermilk to the butter mixture in three additions, mixing just until combined after each.

Divide the batter evenly between the prepared cupcake liners, filling them about 3/4 full.

Bake for 18-20 minutes, until a toothpick inserted in the center comes out clean or with just a few moist crumbs.

Allow cupcakes to cool in pans for 10 minutes, then transfer to a wire rack to cool completely.

Place the chocolate chips, heavy cream and corn syrup (if using) in a microwave-safe bowl.

Microwave in 20-second intervals, stirring well between each, until melted and smooth.

Sift in the confectioners' sugar and whisk until fully incorporated.

Let ganache sit for 10-15 minutes to thicken slightly before using.

Once cupcakes are completely cooled, use a paring knife to cut a cone-shaped cavity out of the center of each, going about 3/4 of the way down but not cutting through the bottom. Remove the cone portion.

Transfer the chilled pastry cream to a piping bag fitted with a round tip. Pipe the pastry cream into each cavity, filling it to the top.

Replace the cone portion back on top of the filling.

Spoon or drizzle the slightly thickened ganache over the tops of the filled cupcakes.

Refrigerate cupcakes until ready to serve. Boston cream cupcakes are best consumed within 4-5 days.