For the strawberry puree (best made a day ahead of time): In a medium size saucepan, heat the strawberries on medium heat. When the strawberries start to soften and juices release, use an immersion blender to puree the strawberries. You can also remove the strawberries from the pan and use a blender or food processor to puree them (be careful of the steam that gets trapped), and then put the puree back into the saucepan over low heat.Continue to cook the strawberry puree until it thickens and the water is reduced. This can take a while, so be patient and do this ahead of time. With frozen strawberries, mine took about 30 minutes to reduce. If needed, you can add a teaspoon of cornstarch to help move the process along. Put a fine mesh sieve over a medium-size bowl. Pour the strawberry puree into the fine mesh sieve. Let it sit for a few minutes. Don’t push the mixture through. This lets the remaining water, if any, filter out. Scoop the puree that is still remaining in the sieve into a heat proof bowl. Measure 2/3 cup for the cake and save the remaining portion in the refrigerator for the buttercream. For the Cake Layers: Preheat your oven to 325 degrees F. Spray three 8-inch round cake pan with cooking spray. Line the bottoms with parchment. Spray again. Set aside.
In a medium sized mixing bowl, whisk together the flour, baking powder, salt, and baking soda. Set aside.
In a mixer fitted with the paddle attachment, beat the sugar, butter, and oil for about 2 minutes. Mixture should get fluffier in texture and lighter in color.
Add the eggs and egg whites, one at a time, and mix well after each addition. Add the vanilla and emulsion/extract, if using. After the eggs are added, turn the mixer to medium-high and beat the cake batter for about 1 to 2 minutes, until the mixture is smooth and fluffy.Stir in the strawberry puree. With the mixer on low, alternatively add the flour mixture with the buttermilk, starting and finishing with the flour mixture. Mix until just incorporated.
Evenly divide the batter between the three pans, about 17 to 18 ounces in each.
Bake the cake layers for about 30 to 35 minutes, until a toothpick inserted in the center comes out with just a few moist crumbs on it.