Preheat the oven to 425 F and line a baking sheet with parchment paper.
Mix the water, milk, butter, sugar and salt together in a medium pot. Bring the mixture to a boil, then remove from heat.
Add the flour and mix well as you put it back on the heat. Once the dough fully forms and pulls away from the sides of the pot, transfer the dough to a medium bowl and mix in the eggs, one at a time.
Use a pastry bag with a large round tip filled with the dough (or if you are using a disposable piping bag, cut out the bottom so the opening it about ½" wide) to pipe out 5" lengths of dough.
Bake for 15 minutes, then prop open the oven with a wooden spoon and bake for an extra 25 minutes. Allow to cool on a wire rack.
While the pastry is baking, mix the egg yolks and the sugar together in a small bowl until light and fluffy. Mix in the flour and cornstarch. Set aside.
Heat the milk in a saucepan until it boils. Slowly pout about ½ cup of the milk into the eggs, stirring constantly. Add the egg mixture into the milk and stir constantly until the mixture thickens.
Add in the vanilla, matcha powder and butter. Allow to cool.
Heat the heavy cream and chocolate over low heat until completely melted. Mix in the butter.
Take the end of a wooden spoon and insert through each of the pastries. Fill a piping bag with the matcha filling and fill each eclair. Dip the tops of each eclair in the chocolate and allow the eclairs to set in the refrigerator for at least 30 minutes to an hour before serving.
Notes
Keep refrigerated. Best served same day, but may store up to three days in an airtight container.
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