Preheat the oven to 375℉. Grease and line an 8x8-inch baking pan with parchment paper.
Make the filling: In a small saucepan over medium heat, combine diced mangos, granulated sugar, and lime juice. Stir until sugar is dissolved. When the mixture boils, reduce heat to low and simmer 8-10 minutes, stirring occasionally until thickened.
Whisk together cornstarch and 3 Tablespoons water in a small bowl. Add to the mango mixture, and stir to combine until a thick jam forms, about 1-2 minutes. Set aside to cool slightly.
Make the crust: In a large bowl, whisk together flour, sugar, baking powder, baking soda, salt, and lime zest. Add the cubed butter, sourdough discard, and egg. Use a fork or pastry cutter to mix the ingredients together. The dough will be crumbly (we love those butter chunks!) but not dry. Press half the dough into the prepared baking pan.
Spread the mango mixture evenly on top of the base crust layer. Crumble the remaining crust mixture on top, making sure you can still see some of the mango layer. Sprinkle with turbinado sugar.
Bake for 40-45 minutes until the top is lightly browned. Let cool at least 1-2 hours before serving. (If you want to speed up the cooling, let cool for 30 minutes at room temperature, then 30 minutes in the refrigerator).
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Notes
To make this recipe with active sourdough starter, replace the sourdough discard with active starter (150g). You will not need to change any other ingredients. If you like a thick fruit layer, double the filling!