FOR THE CANDIED ALMONDS:
Preheat oven to 300 degrees and line a baking sheet with a Silpat or parchment paper and set aside.
In a small bowl mix sugar and sea salt. In a separate mixing bowl whisk together egg white, vanilla and water until it becomes foamy. Add almonds to egg white mixture and toss to combine, making sure to evenly coat all of the almonds. Add the sugar mixture and toss to combine, coating almonds completely.
Spread almonds evenly on prepared baking sheet. Place in oven and bake for 15 minutes. Stir and toss almonds and bake for another 15 minutes. If your almonds are not yet a nice golden brown colors and needs some additional baking time. Toss and stir almonds and bake another 5-10 minutes, keeping an eye on them making sure not to overcook or burn.
Remove almonds from oven and toss continuously for a few minutes to prevent clumping, then allow to cool completely on sheet pan.
Store in an air-tight container if not using the same day (can be stored up to one week).
FOR THE FILLING:
Whisk egg yolks, 1 tablespoons sugar, and cornstarch in medium bowl until mixture is pale yellow and thick, about 1 minute; set aside.
Heat milk, salt, and remaining 4 tablespoons sugar in medium saucepan over medium heat until simmering, stirring occasionally to dissolve sugar.
Gradually whisk half of milk mixture into yolk mixture to temper. Return milk-yolk mixture to saucepan. Return to simmer over medium heat and cook, whisking constantly, until mixture is thickened, about 1 minute.
Off heat, whisk in butter and vanilla.
Transfer mixture to clean bowl, press parchment paper directly onto surface, and refrigerate until set, at least 3 hours and up to 2 days. (see assembly step for addition of heavy cream and almond extract.)
FOR THE CAKE:
Adjust oven rack to middle position and heat oven to 350 degrees. Grease four 10” x 4” loaf pans or two 9” round cake pans, line bottoms with parchment paper, grease parchment, and flour pans.
Mix milk, egg whites, vanilla and almond extracts together in 2-cup liquid measuring cup. Using stand mixer fitted with paddle, mix flour, sugar, baking powder, and salt on low speed until combined. Add butter, 1 piece at a time, and mix until only pea-size pieces remain, about 2 minutes.
Add half of milk mixture, increase speed to medium-high, and beat until light and fluffy, about 30 seconds. Reduce speed to medium-low, add remaining milk mixture, and beat until incorporated, about 15 seconds (batter may look slightly curdled). Give batter final stir by hand; do not overmix.
Divide batter evenly between prepared pans and smooth tops with rubber spatula. Bake until tops are light golden and toothpick inserted in center comes out clean, 18 to 22 minutes (for 10” x 4” pans) or 20 to 25 minutes (for 9”round pans), rotating pans halfway through baking. Let cakes cool in pans on wire rack for 10 minutes. Remove cakes from pans, discarding parchment, and let cool completely on rack.
FOR THE FROSTING:
Put the butter and shortening in the bowl of a stand mixer fitted with the paddle attachment. Mix on medium speed for about 2 minutes, scraping down sides of bowl about halfway through.
With the mixer off, add in the sugar, salt, half and half, corn syrup, and almond extract. Turn the mixer onto low speed until all the ingredients are just combined. Turn mixer up to medium-high and let mix for another 5 minutes, scraping down the sides of bowl as needed. The frosting should be light but still relatively stiff.
ASSEMBLY:
Remove the filling from the refrigerator and stir well.
Place the heavy cream and almond extract in the bowl of a stand mixer fitted with a whisk attachment. Whip on high speed until stiff peaks form. Gently fold whipped cream into the filling using a large rubber spatula. Set aside.
Place about half of the frosting in a pastry bag fitted with a large round tip (we use ATECO #805). Place one cake layer on serving platter. (If you are using 8” rounds, you will need to cut each in half horizontally to make four layers.) Pipe a “dam” of frosting all the way around the cake perimeter. Spread about 1/3 cup of the filling inside of the frosting “dam” and smooth to completely cover the cake layer. Top with additional cake layer and repeat 2 more times. (8” rounds will require a bit more filling. You will have filling left over either way, which can be stored in the refrigerator for several days.) Top with final cake layer and spread the remaining frosting evenly over the sides and top of cake. It does not need to be pretty, just well covered!
Immediately press candied almonds onto the sides and top of the cake to cover completely. (You may have some almonds left over which are great for snacking or as a salad topping.)
Refrigerate uncovered for at least two hours before serving.