Tres Leches Cake

For the condensed milk:
Place the milk in a heavy-bottomed saucepan and bring to a rapid simmer over medium-high heat. Reduce the heat to medium and simmer the milk, stirring frequently, for approximately one hour and 15 minutes, until it has reduced by slightly more than half to about 1¼ cups. Remove 3/4 of a cup of the milk and set it aside. Add the sugar to the remaining milk in the saucepan and bring it to a simmer, stirring constantly to avoid scorching. Simmer until the sugar has dissolved and the mixture thickens enough to coat the back of a spoon, about 10 minutes. Remove the saucepan from the heat and stir in the butter and vanilla. Pour into a heat-proof container. Add the reserved 3/4 of a cup of reduced milk. Use immediately or cool to room temperature, cover, and refrigerate for up to two days.

For the cake:
 

Preheat an oven to 350°F.
Spray the bottom and sides of a round cake pan three inches deep and nine inches round with nonstick baking spray, then lightly flour it.

Sift together the flour, baking powder, and cinnamon in a medium bowl. Stir in the salt and set aside.

Put the eggs and sugar in the bowl of a stand mixer with a whisk attachment. Whisk to combine, then whisk on high speed until the mixture becomes light and fluffy, about five minutes. Reduce the speed to medium-low and alternate adding the flour mixture and the milk a third at a time, scraping the bowl after each addition. Remove bowl from the mixer, scrape the bottom and sides, and immediately pour the batter into the prepared pan. Bake 20 to 25 minutes until the cake is set and a toothpick inserted into the center comes out clean.

Remove the cake from the oven and sit it on a rack to cool to room temperature. Remove the cake from the pan and place it on a large dinner plate. Using a long serrated knife, trim the top crust off the cake, exposing the cake’s inner crumb structure. (What you trim should be so thin that it crumbles. Cook’s treat!)

Pour the condensed milk into a four-cup measuring cup; add enough cream to bring the measurement to two cups. Add the rum and vanilla and stir to combine. Slowly pour the mixture over the cake, letting the cake absorb the liquid. If the cake stops absorbing the mixture, pause for a minute, then continue until the entire two cups of liquid is absorbed. Place the cake in the refrigerator while the meringue is being prepared.

For the meringue:
 

Place the water and sugar in a small saucepan and bring to a boil over medium-high heat. Using a candy thermometer to measure, boil the sugar syrup until the temperature reaches 235°F.
While the syrup is boiling, put the egg whites in a medium mixing bowl. Using a hand mixer with a whip attachment, whip the egg whites until they begin to froth. While still whipping, slowly pour the sugar syrup down the side of the bowl. Continue whipping the whites until they reach room temperature and form soft peaks. Scrape the bowl.

Remove the soaked cake from the refrigerator and place it on a cake platter with a rim. (Sometimes a little milk will drip out when the cake is cut.) Using an offset spatula, spread the meringue all over the top and sides of the cake, moving back and forth with your wrist to give the meringue peaks. Once the cake is completely coated in meringue, use a kitchen torch to slightly brown the peaks of the meringue. Serve immediately.