Blend the hulled strawberries until completely smooth, then pour the puree into a saucepan. Simmer over medium heat, stirring often, for 20 to 25 minutes, until thick and reduced to about 2/3 cup.Transfer to a bowl and let it cool completely.
Preheat the oven to 350°F, then grease two 9-inch round cake pans and line the bottoms with parchment paper. In a medium bowl, whisk together the cake flour, baking powder, baking soda, and salt.
In a large bowl, beat the butter and sugar on medium-high speed for 3 to 4 minutes, until pale and fluffy. Gradually add the egg whites, beating well after each addition, then beat in the vanilla.
Stir 1/2 cup of the cooled strawberry reduction into the almond milk along with the food coloring, if using, and reserve the rest for the frosting. With the mixer on low, add the flour mixture in three additions, alternating with the strawberry milk, beginning and ending with the flour.
Divide the batter between the pans and bake for 25 to 30 minutes, until a toothpick comes out clean. Cool in the pans for 10 minutes, then turn out onto a wire rack to cool completely.
For the frosting, blend the freeze dried strawberries into a fine powder. Beat the butter for 2 minutes until creamy, gradually add the powdered sugar and strawberry powder, then add the reserved strawberry reduction, vanilla, and salt and beat for 3 minutes until fluffy.
Place one cake layer on a serving plate, spread with frosting, and top with the second layer. Frost the top and sides, arrange the fresh strawberry halves on top, and chill for 20 minutes before slicing.