Melt the 4 ounces of butter in a medium-sized saucepan over medium heat. As the butter melts, whisk it frequently until foam begins to appear. Once you see the foam, whisk constantly until the butter begins to brown and it smells nutty and fragrant. Butter can go from brown to burnt very quickly so do not leave it unattended. Remove from the heat and allow to cool. There should be approximately 1/2 cup liquid. Set aside.
Preheat the oven to 350 degrees F. Place an oven rack in the middle position. Lightly spray the bottom of 3 8-inch cake pans with baking spray and then cover them with parchment rounds. Set aside.
Whisk together the flour, cornstarch, baking powder and salt in a medium bowl. In a separate small bowl, combine the half and half, bourbon and vanilla extract.
In a stand mixer with the paddle attachment, cream the 8 ounces room temperature butter and sugar together on low speed for 3-4 minutes, then turn the heat up to medium-high and cream for an additional 2-3 minutes. On low speed, add the eggs, one at a time, allowing each egg to incorporate before adding the next. Scrape down the sides of the bowl. With the mixer still on low speed, quickly alternate between adding the dry ingredients, the browned butter (make sure to scrape out the brown bits), and the liquid ingredients (ending with the dry) until just combined. Scrape down the sides well, making sure to reach the bottom of the bowl.
Distribute the batter evenly between the 3 prepared cake pans, using a spatula to even out the tops. If you want to make sure the cakes are very even in size use a kitchen scale.
Bake until the a toothpick comes out of the center of each cake clean, approximately 32-37 minutes. Allow the cakes to cool completely in the pan before removing.
Prepare the buttercream:
Place the sugar and water in saucepan with a tight fitting lid. Turn the heat on high and cover.
While the sugar syrup is heating up, place the egg whites in the bowl of a stand mixer fitted with the whisk attachment. Beat on high speed until a soft peak forms, then turn down the speed to medium.
Once the sugar syrup is simmering, remove the cover from the pan and turn the heat down slightly to medium high. Cook the syrup for 5 minutes (until a candy thermometer reached 235-240 degrees F) and then slowly and carefully pour it down the side of the mixing bowl into the meringue while the machine is still mixing. Add the syrup very slowly to avoid scrambling the eggs.
Once the syrup is added, turn the mixer back up to high and allow the meringue to cool as it whips. This can take up to 20 minutes.
Once the meringue has cooled to room temperature, slowly add the butter one piece at a time. The meringue will deflate slightly.
Once all of the butter is incorporated, slowly drizzle in the bourbon and sprinkle in the salt. You can push these flavors as much as you like.
Assemble the cake:
Place the first layer of cake on a revolving cake stand and remove the parchment paper. Placing a cardboard round below the cake is optional but will make transporting the cake easier after it is assembled.
Spread approximately one cup of buttercream on the cake and spread it around evenly with an offset spatula. Add more buttercream as needed to reached the desired thickness. Repeat with the second and third layer (don't forget to remove the parchment each time). Use an offset spatula to apply a thin layer of frosting to the side and top of the cake. Chill in the refrigerator for 30 minutes to set this first layer of buttercream. Cover the entire cake with a final layer of frosting.