Cut 3 tablespoons unsalted butter into 3 pieces and place in a small microwave-safe bowl. Microwave in 20-second bursts until mostly melted, 40 to 50 seconds total (it will melt completely as it sits).
Place ⅓ cup granulated sugar, 1 large egg, and ⅛ teaspoon kosher salt in a medium microwave-safe bowl and whisk until smooth. Add ⅓ cup key lime juice and the melted butter, and stir to combine. Microwave on high power in 1-minute intervals, whisking after each, until it thickens and coats the back of a spoon, 3 to 4 minutes total.
Finely grate the zest of ½ medium lime into the curd and whisk to combine. Press a sheet of plastic wrap directly onto the surface of the curd and refrigerate until thickened, at least 45 minutes (it doesn’t need to be fully cold). If you’re strapped for time, cool the curd faster by placing it in an ice bath.
Place 1 (3.4-ounce) box instant vanilla pudding mix and 1 ¾ cups cold milk in a large bowl and whisk until smooth. Add the key lime curd and whisk until smooth.
Place 2 cups cold heavy cream, 3 tablespoons powdered sugar, ¾ teaspoon vanilla extract, and ⅛ teaspoon kosher salt in the bowl of a stand mixer fitted with the whisk attachment. (Alternatively, use a large bowl and electric hand mixer or whisk by hand.) Beat on low speed, increasing to high speed, until stiff peaks form, 2 to 3 minutes.
Transfer 1 cup of the whipped cream into the key lime custard and fold together with a flexible spatula until just combined. Add 1 more cup of the whipped cream and fold together until just combined and no streaks remain.
Arrange graham crackers in the bottom of an 8x8-inch, 2-inch deep baking dish, breaking them as needed to fit into a single tight, even layer. Evenly spread ⅓ of the pudding mixture (about 1 ¼ cups) over the crackers. Repeat layering the graham crackers and pudding mixture 2 more times. Dollop the remaining whipped cream on top and spread into an even layer.
Cover and refrigerate for at least 8 hours or up to 2 days before serving. Finely grate the zest of ½ medium lime over the delight just before slicing into 9 pieces and serving.