1. In a saucepan, heat the heavy cream and whole milk over medium heat until it begins to simmer.
2. In a bowl, whisk together the sugar and matcha powder.
3. In another bowl, whisk the egg yolks. Gradually add the sugar and matcha mixture, whisking constantly until well combined.
4. Slowly pour the hot cream mixture into the egg yolk mixture, whisking constantly to prevent the eggs from curdling.
5. Return the mixture to the saucepan and cook over low heat, stirring constantly, until it thickens and coats the back of a spoon.
6. Strain the mixture through a fine-mesh sieve into a bowl and let it cool to room temperature.
7. Cover the bowl and refrigerate for at least 2 hours or overnight.
8. Churn the mixture in an ice cream maker according to the manufacturer's instructions.
9. Transfer the ice cream to a container and freeze until firm, about 4 hours.