For the Cheesecake:
Preheat your oven to 325°F (165°C).
Using a countertop mixer fitted with the paddle attachment, beat the cream cheese on medium speed until completely smooth, about 3 minutes.
Add the sugar and flour, mixing until well combined.
Whisk the eggs and egg yolk together, then add them to the bowl in two additions, mixing fully after each addition.
Add the sour cream and vanilla extract, mixing until fully combined. Be sure to scrape the sides and bottom of the bowl to ensure everything is mixed evenly.
Spray a 9-inch springform pan with nonstick baking spray, line the bottom with parchment paper, and pour the cheesecake batter into the pan.
Wrap the bottom of the springform pan with aluminum foil and place it in a large rimmed baking pan. Create a water bath by filling the pan with about 1 inch of water.
Bake for 30-35 minutes, until the center of the cheesecake is just barely set. A 1-inch ring of “looser” filling in the center is ideal.
Remove the cheesecake from the oven, let it cool slightly, then wrap the entire pan in plastic wrap and freeze overnight.
For the Cake:
Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans, and line the bottoms with parchment paper.
In a large bowl, sift together the flour, baking powder, and salt. Set aside.
Using a countertop mixer fitted with the paddle attachment, cream together the butter and sugar on medium speed until light and fluffy, about 2-3 minutes.
Add the egg and egg whites, mixing on low speed until well combined.
Add half of the flour mixture, mixing on low speed until well incorporated.
Add the milk, sour cream, vanilla extract, and almond extract, mixing until well combined.
Add the remaining flour mixture and mix on low speed until fully combined. Scrape down the sides of the bowl as needed.
Gently fold in the rainbow sprinkles.
Divide the cake batter evenly between the two prepared pans.
Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean.
Let the cakes cool in the pans for 10 minutes before transferring them to a cooling rack to cool completely.
For the Frosting:
Using a countertop mixer fitted with the paddle attachment, beat the cream cheese and butter together until well combined.
Add the vanilla extract and powdered sugar, one cup at a time, until the frosting reaches your desired sweetness.
Beat the frosting on medium-high speed for 3-4 minutes until it becomes fluffy.
Fold in the rainbow sprinkles.
To Assemble the Cheesecake Cake:
Place one layer of cake on a large plate or cake stand. Spread ½ cup of frosting evenly over the top.
Remove the cheesecake from the freezer and place it on top of the frosted cake layer.
Spread another ½ cup of frosting over the cheesecake layer.
Place the second cake layer on top of the cheesecake.
Frost the top and sides of the cake using the remaining frosting.
Decorate the top of the cake with additional rainbow sprinkles.
Refrigerate the cake until ready to serve.