In a separate medium bowl, whisk together the egg yolks. Slowly pour the warm mixture into the egg yolks, whisking constantly, then scrape the warmed egg yolks back into the saucepan. Stir the mixture constantly over medium heat with a heatproof spatula or wooden spoon, scraping the bottom as you stir, until the mixture thickens and coats the spatula.
Pour the custard through the strainer and stir it into the cream, then whisk it vigorously until custard is frothy to dissolve the green tea powder. Stir until cool over an ice bath. Chill the mixture thoroughly in the refrigerator, then freeze it in your ice cream maker according to the manufacturer's instructions.