Preheat the oven to 350°F. Line a muffin tin with cupcake liners.
In a large bowl, cream together the softened butter and sugar until light and fluffy. Add the eggs one at a time, mixing well after each addition. Stir in the milk and vanilla extract.
In another bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Divide the batter evenly among the cupcake liners, filling each about two-thirds full. Bake for 18-20 minutes or until a toothpick inserted into the center comes out clean. Let the cupcakes cool completely.
While the cupcakes are cooling, prepare the pastry cream. In a saucepan over medium heat, combine the milk and half of the sugar. In a separate bowl, whisk together the remaining sugar, cornstarch, and egg yolks until smooth. Once the milk is hot, slowly pour it into the egg mixture while whisking constantly. Return the mixture to the saucepan and cook over medium heat, stirring continuously until it thickens. Remove from heat and stir in the butter and vanilla extract. Transfer to a bowl, cover with plastic wrap, and refrigerate until chilled.
For the chocolate ganache, heat the heavy cream in a small saucepan until just simmering. Pour it over the chocolate chips in a bowl and let it sit for 2-3 minutes. Stir until smooth and glossy.
Once the cupcakes are completely cool, use a small knife to cut a cone-shaped piece from the center of each cupcake. Fill the hole with the chilled pastry cream and replace the top.
Drizzle the chocolate ganache over the filled cupcakes. Allow the ganache to set for a few minutes before serving.