Preheat oven to 350°F. Line 3 9-inch round cake pans with parchment paper and spray them with baking spray. Set aside.
In a medium-sized bowl, combine the flour, baking powder, baking soda, and salt. In a large bowl, whisk together the sugar, strawberry puree, yogurt, vegetable oil, and eggs. Add in the flour mixture and whisk just until combined.
2¾ cups cake flour, 1½ teaspoons baking powder, 1½ teaspoons baking soda, 1¼ teaspoons kosher salt, 2 cups granulated sugar, 1 cup strawberry puree, ½ cup plain yogurt, ½ cup vegetable oil, 3 large eggs
Evenly divide the batter between the 3 baking pans (about 448 grams per pan) and place into the preheated oven to bake for 25-28 minutes, or until a toothpick inserted comes out clean or with moist crumbs.
While the cakes are baking make the strawberry compote. Add all of the compote ingredients to a medium saucepan set over medium-low heat and allow to simmer for 8-10 minutes. Be sure to stir it constantly to avoid burning or scorching it. The strawberries should cook down and the sauce will turn into a sort of syrup. Once the compote is cooked, pour into a bowl to cool.
4 cups chopped strawberries, 1 cup granulated sugar, 2 tablespoons lime juice, ½ teaspoon kosher salt
Once the cakes are baked, remove from the oven and place them onto a cooling rack to cool.
While the cakes and compote are cooling, make the cream cheese frosting by placing all of the frosting ingredients into the bowl of a stand mixer fitted with a whisk or paddle attachment. Whisk on low for a minute to allow the powdered sugar to incorporate. Increase to high speed and let whip for at least 4 minutes to create a smooth frosting. Fill a piping bag fitted with a tip with ⅓ cup of frosting.
½ cup unsalted butter, ¾ teaspoon pure vanilla extract, ½ teaspoon kosher salt, 12 ounces cream cheese
Once the cakes are cooled, place one layer onto a plate or cake stand. Pipe a circle of frosting onto the edge of the cake to contain the strawberry compote. Spoon ⅓-½ cup of compote into the middle of the frosting ring and spread out. Top with a second layer of cake and repeat the frosting ring and compote steps before topping with the last layer of cake.
Spread a thin layer of frosting onto the top and sides of the cake. Pour the remaining compote onto the top of the cake and allow the syrup to run down the sides of the cake. Spoon the remaining frosting into the piping bag and pipe little swirls onto the top edge of the cake in a circle formation.
Once frosted, slice and serve!