1. To make the mango frozen yogurt, whisk together the mango puree, sugar, yogurt and lime juice until the sugar is dissolved. Chill thoroughly, then freeze in your ice cream maker according to the manufacturer’s instructions.
2. To make the blueberry compote, heat the blueberries in a nonreactive saucepan with the sugar, lemon zest, and water until the blueberries soften and release their liquid.
3. Dissolve the corn starch or potato starch in the 2 tablespoons of lemon or lime juice and add to the blueberries. Cook until the berry mixture begins to boil, stirring occasionally.
4. Remove the blueberries from the heat and let cool until room temperature. The compote will thicken as it cools.