Purée mangoes in blender or food processor on high for 30 seconds until smooth. Strain and measure out 1 1/2 cups of purée; reserve remainder for another use.
In a medium bowl, whisk mango purée, yogurt, sugar, and lime zest until well combined and the sugar doesn't feel gritty anymore.
Add lime juice in 1/2 teaspoon increments and kosher salt in 1/4 teaspoon increments, tasting frequently.
Mixture should be a little tart with a hint of saltiness.
If mangoes started at room temperature, chill mixture in refrigerator for 1 hour until cold. Churn in ice cream maker according to manufacturer's instructions.
Transfer frozen yogurt to airtight container and chill in freezer for at least 3 to 4 hours before serving.
