Make the pastry cream. In a heavy saucepan, stir together the milk and 2 tablespoons of sugar. Bring to a boil over medium heat, being careful not to scald. Remove from heat and let cool slightly.

Whisk together the egg yolk and egg in a bowl. Add the remaining tablespoon of sugar and cornstarch, whisking until smooth. Gradually add milk in a thin stream, whisking constantly.

Return the mixture to the saucepan and add vanilla beans and pod. Cook over low heat, stirring often until the mixture begins to thicken and coats the back of a wooden spoon. Take care not to let the eggs curdle. Remove from the heat and stir in the butter, mixing until the butter is completely blended in. Remove vanilla pod, transfer to a bowl, cover with plastic wrap and refrigerate until chilled.

Make the choux. Preheat oven to 400 degrees. Line a baking sheet with parchment paper. Sift together the flour, sugar and salt in a bowl and set aside.

Add the butter and water to a saucepan and bring to a boil over medium heat. Remove from heat and, with a wooden spoon or spatula, quickly add the flour mixture. Return to heat and stir constantly until the dough begins to pull away from the sides of the pan- this should only take about 1-2 minutes. Remove from heat.

Transfer the dough to an electric mixer and beat on low speed for a couple of minutes to release the steam from the dough. Add the 2 beaten eggs and continue to mix until the dough is smooth and shiny.

Spoon or pipe 12 mounds of dough onto the baking sheet, spaced a couple of inches apart. Smooth the top of each mound by lightly tapping with a wet fingertip. Gently brush the remaining beaten egg on the tops of the dough with a pastry brush.

Bake for 15 minutes, then reduce the oven temperature to 350 degrees. Continue baking for an additional 30 to 40 minutes or until the shells are golden. Turn the oven off and open the oven door slightly for about 10 minutes to let the shells dry out a bit more. Remove from the oven and transfer to a wire rack to cool completely.

Make the chocolate ganache. Place the chopped chocolate in a medium sized heat proof bowl and set aside. Heat the cream and butter in a small saucepan over medium heat. Bring to a boil, then immediately pour the boiling cream over the chocolate and allow to stand for 5 minutes. Whisk until smooth.

To assemble the profiteroles, slice the tops off of each pastry shell, fill with pastry cream and replace the top. Drizzle with warm chocolate ganache. Serve immediately.