To make the reduced strawberry puree: Add the quartered strawberries to a food processor or blender and blend until smooth, you should end up with 2 cups of strawberry puree.
Pour the strawberry puree into a large saucepan and place it over medium heat. Cook until the mixture has reduced to ¾ cup (190 grams), stirring often so that the mixture doesn’t burn. This will take about 30 to 35 minutes.
Remove from the heat, scoop the reduced strawberry puree into a heat-proof bowl, and set aside to cool completely.
To make the strawberry cake: Preheat the oven to 350°F (180°C). Spray two 9-inch round cake pans with nonstick cooking spray, line the bottom of the pans with parchment paper, and set aside.
In a large mixing bowl, whisk the cake flour, baking powder, baking soda, and salt together until well combined. Set aside.
In a separate large mixing bowl or measuring cup, whisk the 3/4 cup of reduced strawberry puree, buttermilk, oil, vanilla extract, strawberry extract, and red food coloring together until well combined. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment or in a large mixing bowl using a handheld mixer, beat the Danish Creamery butter on low speed until smooth, then slowly mix in the granulated sugar.
Once all of the sugar is added, increase to medium speed and continue mixing for another 4 to 5 minutes or until the mixture is light and fluffy.
Mix in the eggs, one at a time, making sure to stop and scrape around the bottom and sides of the bowl after each egg.
Add the dry ingredients in three additions alternating with the strawberry buttermilk mixture (begin and end with the dry ingredients) on low speed. Mix in each addition until just combined, making sure not to over mix the batter.
Use a rubber spatula to scrape around the bottom and sides of the bowl to ensure that everything is well combined.
Evenly divide the batter between the two prepared cake pans and spread it around into one even layer.
Bake for 28 to 32 minutes or until a toothpick inserted into the center of the cakes comes out clean. Remove from the oven and allow to cool in the pans for about 20 minutes. Slide a knife around the outside of the cakes, then carefully remove the cakes from the pans, and transfer to a wire rack to cool completely.
To make the strawberry frosting: In the bowl of a stand mixer fitted with the paddle attachment or in a large mixing bowl using a handheld mixer, beat the Danish Creamery butter on medium speed until smooth.
Mix in the powdered sugar on low speed, one cup at a time, making sure to mix well after each addition.
Add the freeze-dried strawberries to a blender or food processor and blend into a fine powder.
Add the strawberry powder, heavy whipping cream, vanilla extract, and salt and mix on low-medium speed until fully combined, making sure to scrape down the sides of the bowl as needed.
To assemble the cake: Level the tops of each cake with a knife or cake leveler. Place one of the cakes on a cake stand, top with a layer of frosting, and smooth it out into one even layer. Place the second layer on top, then use the remaining frosting to frost the top and sides of the cake.
Store cake in an airtight container at room temperature for 2 to 3 days or in the refrigerator for up to 4 days.