Combine grated lemon zest, 3/4 cup whole milk, and 1/4 cup of the sugar in a medium saucepan and heat over medium-low heat until just hot.
While the lemon zest/milk/sugar mixture is heating, whisk together 4 egg yolks, the remaining 1/4 cup of sugar, and 1/2 teaspoon salt until well combined, then whisk in 2 tablespoons cornstarch, then 1/2 cup lemon juice.
Slowly whisk a third of the hot milk mixture (from the first step) into the yolk mixture (from the second step). Pour the mixture back into the saucepan with the rest of the hot milk mixture and cook over medium-low heat, whisking steadily until the custard begins to thicken and bubble for 1 minute. You'll need to stop whisking to check if it's bubbling. Be warned — it'll take a good 5 or 10 minutes for the custard to thicken, so be patient and don't make the mistake that I did!
Once the custard has thickened, strain the custard through a fine mesh sieve into a clean bowl and whisk in 1/2 cup cubed cold butter until it has melted.
Once the butter has been fully incorporated into the custard, place a piece of plastic wrap directly upon the surface of the custard and place in the refrigerator to cool for about 2 hours — it'll thicken more and set once it cools. Note that you have to wait for the custard to set in order to top the cake.