In the plastic bowl, whisk together the Greek yogurt, whole milk, heavy whipping cream, granulated sugar, and vanilla extract. Stir in the mango chunks, then cover and chill in the refrigerator at least 4 hours to overnight.

About 30 minutes before churning, put the yogurt mixture in the freezer to get it really cold. Churn in your ice cream freezer according to the manufacturer’s directions. Add the blueberries a little at a time during the last 2 minutes of churning. Scoop the frozen yogurt into the plastic freezer container, press a piece of plastic wrap over the yogurt, and put the lid on. Freeze until firm, at least 2 hours, before serving.