Pre-heat 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.
Using your fingers and the bottom of a glass or dry measuring cup, press the crumbs firmly into the bottom and up the sides of a 9 x 1.5-inch pie pan; the crust should be about ¼-inch thick.
Bake for 10 minutes, until just slightly browned.
Remove from oven and let the crust cool on a wire rack.
To prepare the filling:
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 thick 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.
To prepare the topping:
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 the lime zest and lime slices.
Store the pie in the refrigerator until ready to serve.
Notes
The crust can be made a day ahead of time; however, the filling should be added on the day of serving, otherwise the crust may get soggy.