Combine strawberries and water in a medium-sized saucepan over medium heat. Cook, stirring occasionally, for 2 to 4 minutes, or until strawberries become soft. Use a potato masher or a rubber spatula to mash the strawberries until mushy and there aren’t any large lumps. Reduce to a simmer, add cornstarch, and stir until dissolved. Cook for 5 to 10 minutes, stirring occasionally, until mixture is thick enough to coat a spoon/spatula and has the consistency of jam or jelly. You should have about 1 cup of compote. It’s okay if the mixture is still slightly thin because it will thicken a little as it cools. Let compote cool completely.
For the cake:
Preheat oven to 350°F. Line three 8-inch cake pans with parchment paper and spray with nonstick spray.
Whisk together flour, baking powder, baking soda, salt, and sugar. Add eggs, oil, vanilla, milk, and strawberry compote. Mix on medium speed with an electric mixer until all ingredients are incorporated, scraping the sides of the bowl as necessary, about 1 minute.
Divide batter evenly among the prepared cake pans. Bake for 18 to 20 minutes or until cakes are lightly golden brown and set in the center. (Test by inserting a toothpick into the center of each cake layer. If it comes out clean, they're done!)
Let cakes cool in pans for about 5 minutes before transferring to a wire rack to cool completely.
For the frosting:
Place the freeze dried strawberries in a food processor and process until finely ground. Press through a mesh sieve and discard larger pieces.
In the bowl of a stand mixer, beat butter and shortening until smooth. Add the ground strawberries, vanilla, and milk (or cream). Mix until well combined; scrape the sides of the bowl to make sure all the strawberry is incorporated.
Add half of powdered sugar and mix on low speed until mostly combined, then medium-high speed until completely combined, about 1 minutes. Repeat with second half of powdered sugar.
Level cake layers with a serrated knife or cake saw. Place one layer on a cake stand or cake plate and spread with a layer of frosting. Arrange a layer of sliced strawberries over the frosting. Repeat with second layer, frosting, and sliced strawberries. Place the third layer on top and cover the whole cake with frosting. Garnish with strawberries and fresh flowers, if desired. Store in the refrigerator.