Make the puree:

• Cook the fresh or frozen strawberries in a small saucepan over medium heat, stirring occasionally, until reduced by half, 10 to 15 minutes. Blend until smooth using an immersion blender; or transfer to a blender and blend.
• Measure out ½ cup plus 2 tablespoons and let cool completely before using.
• Preheat the oven to 350°F (175°C). Grease two or three 8-inch round cake pans and line the bottoms with parchment paper. Three pans will give you thinner, more elegant layers, while two pans will give you thicker, bakery-style layers.

Make the batter:

• In a medium bowl, whisk together the cake flour, baking powder, baking soda, salt, and freeze-dried strawberry powder.
• In a stand mixer fitted with the paddle attachment, beat the sugar, butter and oil on medium-high speed for 3 to 5 minutes, until pale and fluffy. Gradually add the egg whites, beating well after each addition and scraping the bowl as needed.
• In a separate bowl, whisk together the reserved strawberry puree, buttermilk, Jell-O powder, vanilla, and strawberry emulsion. With the mixer on low, add the dry ingredients and the butter alternating additions, beginning and ending with the dry ingredients. Mix just until combined.
• Divide the batter evenly between the prepared pans and smooth the tops. Bake for 22 to 27 minutes, until a toothpick inserted into the center comes out with just a few moist crumbs. If using two pans, bake for 30 to 35 minutes. Let the cakes cool in the pans for 10 minutes, then transfer to a wire rack to cool completely before frosting.

Make the frosting:

• In a large bowl, beat the butter on medium speed until smooth and creamy, 1 to 2 minutes. Add the cream cheese and beat on medium-high until light and fluffy, 2 to 3 minutes. Add the powdered sugar and freeze-dried strawberry powder and mix until combined. Add the vanilla, strawberry emulsion, cream, and salt and beat until light, fluffy, and spreadable.

Assemble and store:

• Place one cake layer on a serving plate or cake stand. Spread a generous layer of frosting evenly over the top. Place the second layer directly on top and frost the top and sides of the cake as desired.