In a heavy-bottomed saucepan, add egg yolks, granulated sugar, cornstarch, and milk. Whisk until well incorporated.
Heat the saucepan on low heat. Bring to a boil while whisking constantly until thickened. Turn off the heat. Add butter and vanilla extract. Whisk until well incorporated.
Pour the pudding into a medium bowl and immediately cover the surface with plastic wrap, making sure the plastic wrap is touching the whole surface. This is to prevent the skin from forming on top. You can also choose to pass the mixture through a sieve to remove any lumps.
Let the pudding cool down to room temperature and then let it chill in the fridge for at least 1 hour.
Assemble
Add heavy whipping cream into a bowl and sift matcha through a fine mesh strainer. Beat on high speed using a mixer or hand whisk until soft peaks form. Set aside.
Remove the chilled pudding from the fridge and beat on high speed using a mixer or hand whisk until smooth with no lumps.
Transfer one-third of the matcha whipped cream to the pudding. Fold with a spatula or beat on low speed until well combined. Add the remaining whipped cream in 2 additions, gently folding it or beat on low speed into the pudding each time.
Cover the bottom of serving glasses, trifle dishes, or containers with the matcha pudding mixture. Top with a layer of vanilla wafers. Arrange banana slices on top of the wafers. Repeat the layers until you run out of space or ingredients. Top the final layer with the matcha pudding mixture.
Cover tightly with plastic wrap and refrigerate for at least 4 hours or overnight. This ensures the cookies have time to soften.
Just before serving, add a dollop of whipped cream on top and garnish with extra vanilla wafers and sliced banana, if desired.