In a medium saucepan off the heat, whisk together the sugar, cornstarch, and salt.

In a separate medium bowl, whisk the egg yolks. Gradually whisk in the milk and heavy cream until combined. Slowly pour the milk mixture into the saucepan with the sugar, whisking constantly.

Cook over medium heat, whisking constantly, until the mixture thickens and comes to a rolling boil. Boil for 1 minute, continuing to whisk.

Remove from the heat and stir in the cubed butter and vanilla extract until smooth. Strain the cream through a fine-mesh sieve into a bowl.

Cover with plastic wrap, pressing it directly onto the surface. Refrigerate for at least 4 hours, or until completely chilled and set.

In a large bowl, use an electric mixer to beat the softened butter with the granulated and powdered sugars on medium-high speed until light and fluffy, about 2-3 minutes.

Beat in the egg and vanilla extract until combined, scraping down the sides of the bowl as needed.

In a separate bowl, whisk together the flour, baking soda, and salt. On low speed, gradually add the dry ingredients to the wet ingredients until just combined.

Cover the dough and chill for at least 30 minutes.

Preheat oven to 350°F (175°C). Line two baking sheets with parchment paper.

Roll dough into 1.5-inch balls and place 2 inches apart on the baking sheets. Use the back of a 1/2 teaspoon measuring spoon to create a deep well in the center of each ball.

Bake for 11-13 minutes, or until the edges are lightly browned. If the centers have puffed up, gently press the wells down again with the measuring spoon while the cookies are still hot. Let cool completely on the baking sheet.

Place the chopped semi-sweet chocolate in a heatproof bowl.

Heat the heavy cream in a small saucepan or in the microwave until it just begins to simmer. Pour the hot cream over the chocolate and let it sit undisturbed for 5 minutes.

Whisk the mixture gently until the chocolate is completely melted and the ganache is smooth and glossy.

Transfer the chilled pastry cream to a piping bag or use a small spoon to fill the well of each cooled cookie.

Spoon about a teaspoon of the warm ganache over the pastry cream filling on each cookie. Let the cookies sit at room temperature for 30-60 minutes for the ganache to set.