Preheat oven to 375 F (190 C). Separate the eggs, placing yolks in a medium bowl, and one egg white in a small bowl. Reserve remaining three egg whites for later use.
Remove the cover and place the crust on a baking sheet. Beat the single egg white with a fork until frothy. Brush over bottom and sides of crust with egg white. Discard any remaining egg white. Bake for 5 minutes. Remove from oven and let cool. (You can actually skip this step if you want. Just add the filling to the unbaked crust. The crust will not be as crispy, but still tastes good.)
While the crust is baking, remove the zest from the limes. (You need about 1 packed tablespoon of zest so you may not need to zest them all.) Juice the limes and put juice in a measuring cup. (Pro tip: If you roll the limes first, you will get juice out of them more easily.) You may need more limes if they aren’t juicy. You can even add lemon juice if needed, but make sure at least half of the juice is lime for best results.
Add lime zest, lime juice and sweetened condensed milk to the bowl with the egg yolks. (You will need to use a spoon to get everything out of the condensed milk can.) Combine well with a whisk. Pour mixture into prepared pie crust, tapping or shaking gently to smooth out.
Place the pie in the oven (still on the baking sheet) and bake for 10-12 minutes or until set. Remove from the oven and cool completely on a wire rack. (About 1 hour.) Cover with the plastic crust cover and refrigerate until ready to serve, at least 4 hours and up to two days. (The crust will get a bit softer as time goes on.)
Immediately before serving, combine 1 cup whipping cream and 1 tablespoon confectioner’s sugar and beat with an electric mixer until desired consistency. (Another pro tip: Chill the cream and the beaters in a metal bowl in the fridge for at least 20 minutes before whipping it and it will whip a bit faster.) You can cover the entire pie with the cream, serve with dollops on each slice, or pipe it on the pie for a more traditional diner look. Garnish with additional lime zest or lime slices if desired.