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Preheat oven to 375 °F and set an oven rack in the middle position.
Combine the graham cracker crumbs, brown sugar, and melted butter. Press the crumbs firmly into the bottom and up the sides of a 9 x 1.5-inch deep-dish pie pan.
Bake for 10 minutes, then let it cool on a wire rack.
For the Filling:
Lower the oven temperature to 350°F.
Whisk together the sweetened condensed milk, yogurt, lime zest, and lime juice. Pour the mixture into the warm graham cracker crust.
Bake for 15 minutes, until almost set. Let it cool at room temperature for 30 minutes, then refrigerate for about 3 hours.
For the Topping:
Beat the heavy cream until soft peaks form. Add the confectioners’ sugar and beat until medium peaks form.
Top the pie with the whipped cream and decorate with lime zest and lime slices.
