Prepare a bowl with a fine-mesh sieve on top to cool the pastry cream.

In a separate bowl, whisk together the cornstarch and sugar. Add the eggs and whisk until smooth. Set aside.

In a small bowl, whisk together the matcha powder and warm water. Strain the mixture through a sieve to remove any clumps and set aside.

In a saucepan, heat the milk and vanilla bean paste over medium-high heat until just under a boil, stirring occasionally to prevent sticking.

When the milk is warmed, slowly whisk 1/3 of the hot milk into the egg mixture. Then pour the egg-milk mixture back into the saucepan with the remaining hot milk. Whisk over medium heat until thickened like lightly whipped cream. Remove from heat and immediately mix in the matcha mixture. Pour the cream through the sieve into the prepared bowl.

Let the cream cool for 10 minutes, stirring occasionally. When the cream reaches 140°F, mix in the butter one piece at a time until smooth. Cover with plastic wrap pressed directly onto the surface and chill in the refrigerator.

Melt the chocolate in a microwave-safe bowl in 30-second increments, stirring each time, until fully melted. Spread the melted chocolate evenly over the cooled pie crust. Chill in the refrigerator for 10 minutes.

While the chocolate hardens, whip the cold heavy cream, vanilla, and sugar in a stand mixer or with a hand mixer until medium peaks form.

Once the chocolate is hardened, spread the pastry cream evenly in the crust.

Top with whipped cream and spread evenly. Dust with matcha powder.

Refrigerate the pie for at least 3 hours before serving.