In a medium bowl, whisk together the matcha powder and 1/4 cup of the sugar until well combined to remove any lumps.

In a separate bowl, whisk the egg yolks until smooth. Gradually add the remaining sugar while whisking until pale and slightly thickened.

In a saucepan over medium heat, combine the heavy cream, milk, and salt. Heat until just steaming but not boiling, stirring occasionally.

Temper the egg yolks by slowly pouring about 1/2 cup of the hot cream mixture into the yolks while whisking constantly. Then pour the yolk mixture back into the saucepan.

Cook over low heat, stirring constantly with a wooden spoon, until the mixture thickens enough to coat the back of the spoon (about 5-7 minutes). Do not let it boil.

Remove from heat and whisk in the matcha-sugar mixture until fully dissolved and smooth. Stir in the vanilla extract.

Strain the mixture through a fine-mesh sieve into a clean bowl. Cover with plastic wrap pressed directly on the surface and chill in the refrigerator for at least 4 hours or overnight.

Churn in an ice cream maker according to the manufacturer's instructions (about 20-25 minutes) until thick and creamy.

Transfer to an airtight container and freeze for at least 4 hours before serving to firm up.