Preheat the oven to 350°F (177ºC). Grease and line three 6-inch or two 8-inch cake pans.
Start by separating 4 large eggs, placing the egg whites in one bowl and yolks in another. Refrigerate the yolks in an airtight container* until you're ready to make the curd (I recommend making it while the cakes are baking). Set the egg whites aside.
In a jar or measuring cup, combine the 1 1/4 Cups (300ml) of whole milk and 1/4 Cup (60ml) of key lime juice. Stir and set aside. It will curdle by the time you add it to the recipe at the end, and the curdling is the chemical reaction we want!
Add the sifted cake flour, baking powder, and salt into a bowl and whisk to combine. Set aside.
Using a stand mixer fitted with the paddle attachment, mix together the sugar and lime zest on low speed until fragrant and well combined, about 1 minute. Add the butter and cream it together with the lime-sugar mixture on medium speed until light and fluffy, 2-3 minutes.
With the mixer on low, add the egg whites one at a time. Add the vegetable oil and vanilla extract, then turn the mixer to high speed and beat for one minute.
Turn the mixer off and add the cake flour mixture all at once. Mix on low speed until just combined, then slowly pour in the key lime-milk mixture. Mix until smooth and fully combined, about 30 seconds.
Pour the batter evenly between the prepared cake pans and bake for 28-32 minutes, until a toothpick inserted into the centers comes out clean or with a few moist crumbs. Cool for 5 minutes before removing the cakes from the pans. Transfer the cake layers to a wire rack to cool completely to room temperature.