For the Crust: Set an oven rack in the middle position and preheat oven to 375 degrees F.
In a medium mixing bowl, combine the graham cracker crumbs, brown sugar, and melted butter and mix well to blend. Using your hands press the crumbs firmly into the bottom and up the sides of a standard 9 x 1.5-inch (deep-dish) pie pan. The crust should be about ¼-inch thick.
Place the pie crust on a baking sheet, place in the oven and bake for 9-10 minutes, until just slightly browned. Remove from the oven and allow to cool.
Lower the oven temperature to 350 degrees F.
For the Filling: In a large mixing bowl, add the sweetened condensed milk, yogurt, lime zest, and lime juice and mix until incorporated. Pour the filling into the par-baked crust. Bake for 10-12 minutes or until the filling is almost set, note: it should wobble slightly. Remove from the oven and let cool for 30 minutes. Once cool, place the tart in the refrigerator to chill thoroughly, about 3 hours.
For the Topping: In the bowl of an electric mixer, such as a KitchenAid, fitted with a whisk attachment, add the heavy cream and beat on high until soft peaks form. Reduce the speed and add the Confectioners’ sugar, beat until medium peaks form.
To finish the pie, top it with the whipped cream using an offset spatula or using a pastry bag fitted with a star tip for a more decorative design. Garnish with the lime zest and lime slices. Refrigerate the pie until ready to serve.