Cream Puffs with Vanilla Pastry Cream

Ingredients :
For the choux pastry:

100 ml (1/2 cup) milk
100 ml (1/2 cup) cold water
1 tablespoon of sugar (20 g)
A pinch of salt
80 g (1/3 cup) unsalted butter
130 g (1 cup) all-purpose flour
3 large eggs
For the vanilla pastry cream:

2 large eggs
150 g (3/4 cup) granulated sugar
10 g (1 tbsp) vanilla sugar (or 1 tsp vanilla extract)
30 g (2 tablespoons) cornstarch
400 ml (1 2/3 cups) milk
50 g (3 1/2 tablespoons) unsalted butter