In a medium saucepan, heat the heavy cream, whole milk, and half of the sugar over medium heat, stirring occasionally, until the mixture just begins to simmer. Remove from heat.

Meanwhile, in a medium bowl, whisk together the egg yolks and remaining sugar until well combined.

Slowly pour the heated cream mixture into the egg yolk mixture, whisking constantly to temper the eggs. Return the mixture to the saucepan.

Cook the mixture over medium heat, stirring constantly with a wooden spoon, until it thickens and coats the back of the spoon, about 5-7 minutes. Do not let it boil.

Remove from heat and whisk in the matcha green tea powder until fully incorporated.

Pour the mixture through a fine-mesh strainer into a clean bowl to remove any lumps or curdled bits.

Cover the bowl with plastic wrap, pressing the plastic wrap directly onto the surface of the custard to prevent a skin from forming. Refrigerate for at least 4 hours or overnight.

Once the custard is chilled, transfer it to an ice cream maker and churn according to the manufacturer's instructions.

Transfer the churned ice cream to an airtight container and freeze for at least 2 hours to firm up before serving.