Combine 1 cup heavy cream, 1 cup whole milk, and 1/2 cup sugar in a heavy saucepan. Bring mixture to a simmer, stirring until sugar dissolves.
Whisk in yogurt, salt, vanilla, nutmeg and cinnamon. Refrigerate until custard is well chilled.
Transfer to an ice cream maker and process until thickened .
Bring sugar, water and salt to a boil in a 2-quart heavy saucepan. Refrigerate until custard is well chilled. Stir until sugar is dissolved.
Cook mixture without stirring, washing down any crystals from side of the pan with a pastry brush dipped in cold water.
Greek yogurt can be found at most your local food stores. If unavailable, place regular yogurt in a cheesecloth lined strainer, place in a large bowl, cover and chill overnight to drain.