3 cups Greek yogurt (not nonfat)
1 teaspoon vanilla extract
⅔ cup plus 1 tablespoon sugar, divided
2 cups blackberries
3 ounces semi sweet chocolate, chopped
1 ounce white chocolate, chopped
Combine yogurt, ⅔ cup sugar and vanilla in a large bowl, preferably one with a pour spout. Refrigerate for 1 hour. Meanwhile, purée blackberries in the bowl of a food processor. Strain the blackberries using a fine mesh strainer, then stir in the remaining tablespoon of sugar. Refrigerate for 1 hour.
Add blackberry purée to the yogurt mixture and stir until combined. Freeze in an ice cream maker according to manufacturer’s directions. Place frozen yogurt in an airtight container and stir in chocolate and white chocolate pieces. Freeze until firm.