Preheat oven to 375 °F and set an oven rack in the middle position.

In a medium bowl, combine the graham cracker crumbs, brown sugar, and melted butter; stir with a fork first, and then your hands until the mixture is well combined. Press the crumbs firmly into the bottom and up the sides of a 9 x 1.5-inch pie pan.

Bake for 10 minutes, until just slightly browned. Let the crust cool on a wire rack.

Lower the oven temperature to 350°F.

In a large bowl, 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 the filling is almost set; it should wobble a bit. Let cool at room temperature for 30 minutes, then place in the refrigerator to chill thoroughly, about 3 hours.

In the bowl of an electric mixer, 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, decorate with lime zest and lime slices, and store in the refrigerator until ready to serve.

Slice the pie into wedges, wiping your knife clean between slices, and serve cold.

You can make the crust a day ahead of time, but the filling should be added on the day of serving to prevent the crust from getting soggy.