How to Make It
Combine half-and-half, evaporated milk, and 1/3 cup sugar in a medium, heavy saucepan. Bring to a simmer over medium heat (do not boil), stirring frequently.
Combine remaining 1/3 cup sugar and yolks in a medium bowl, stirring with a whisk. Gradually whisk about one-fourth of milk mixture into yolk mixture; slowly whisk in remaining milk mixture.
Return milk mixture to pan; cook over medium-low heat 2 minutes or until mixture slightly thickens, stirring constantly. Remove from heat; whisk in matcha and vanilla. Add tahini; whisk until well blended. Strain mixture through a sieve into a bowl; place bowl in a large bowl filled with ice water. Let stand 15 minutes or until cool, stirring occasionally.
Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer’s instructions. Serve right away (for a soft-serve texture), or spoon into a container, and place in freezer for 1 to 2 hours (for a firmer texture).