To a large blender add the 1 cup heavy whipping cream, 1 (32-ounce) container full-fat vanilla Greek yogurt, 1 tablespoon vanilla bean paste, and 1 cup granulated sugar, and blend until completely combined.
Pour the mixture into a prepared ice cream maker and follow the ice cream maker's directions to chill the yogurt.
Once it is done, you can transfer the mixture to an airtight container and freeze it to make a more solid mixture or eat it right away.