Set up your workstation by placing a fine-mesh sieve over a clean, medium-sized bowl; set this aside for later use.
In a sturdy medium saucepan, gently whisk together the lime zest, key lime juice, granulated sugar, and eggs until well combined. Stir in the unsalted butter.
Place the saucepan over medium-low heat. Cook the mixture, stirring almost constantly, until it visibly thickens and can coat the back of a metal spoon. It should reach a very gentle simmer, but avoid bringing it to a rolling boil.
Immediately remove the saucepan from the heat and pour the warm pudding through the prepared sieve into the bowl below. This step ensures an incredibly smooth and luscious texture, free of any small cooked egg bits.
Cover the bowl tightly with plastic wrap, pressing it directly onto the surface of the pudding to prevent a skin from forming. Place the bowl in the refrigerator for at least 2 hours, or until the pudding is thoroughly chilled and set.
Once the pudding is cold, in a separate mixing bowl, combine the heavy cream and confectioners' sugar. Using an electric mixer (stand or hand-held), whip the cream until it forms stiff, airy peaks.
Carefully fold the whipped cream into the chilled key lime pudding until it’s fully incorporated and the pudding has a light, cloud-like consistency.
Serve this refreshing dessert right away, or keep it refrigerated until you're ready to enjoy. It stays wonderfully fresh for up to 48 hours.