In a large bowl, combine 350g cream cheese, 80g powdered sugar, and 10g cornstarch. Use a hand mixer or whisk to beat until smooth and lump-free.

Add 3 eggs and 2 egg yolks in portions, mixing thoroughly after each addition to ensure the mixture is completely smooth and combined.

In a separate bowl, whisk 20g matcha powder with 50g hot water until fully dissolved with no lumps. Gradually add 170g warm cream in two additions, stirring until well mixed.

Pour the matcha cream into the cheese batter and fold with a spatula until combined. Strain the mixture once to remove any lumps.

Pour the batter into a 6-inch mold (lined with parchment or greased). Bake at 230°C (446°F) for 25 minutes in a preheated oven. Let cool completely.

In a bowl, mix 100g glutinous rice flour, 30g sugar, 30g cornstarch, and 180g milk. Whisk until smooth.

Strain the batter into a heatproof bowl, cover with plastic wrap, and poke a few holes on the surface. Steam over boiling water for 25 minutes on medium heat.

Let the mochi cool until warm, then knead until smooth. Add 3g matcha powder and knead again until the color is even.

Divide the mochi into 6 equal pieces. Roll each into a thin circle.

Cut the cooled Basque cheesecake into 6 portions. Place one in the center of a mochi round and wrap, sealing the edges tightly.

Dust the surface with a bit of matcha powder before serving.