Make the Strawberry Reduction: Using a food processor, purèe the strawberries (you’ll end up with 1/3 Cup of purèe). Add the strawberry purèe into a small saucepan set over medium heat. Bring to a boil, then reduce the heat to low and simmer for 10-15 minutes, until it becomes jam-like and has reduced by more than half. You’ll end up with about 2 1/2 Tablespoons (37g) of reduced purèe after this step, if you have more than that, keep cooking until it's reduced to 2 1/2 Tbsp. Let it cool completely to room temperature (this takes 20 min in the refrigerator) before moving on in the recipe.
Preheat the oven to 350ºF and prepare three 4-inch or one 6-inch cake pan by spraying the sides with cooking spray and fitting the bottom(s) with a wax paper or parchment paper cake circle.
In a medium sized bowl, place the sifted cake flour, baking powder, and salt. Whisk to combine and set aside.
In the bowl of your stand mixer with the paddle attachment, whip the butter on high until creamy, 2 minutes. Add the granulated sugar and beat together with the butter at medium speed until light and fluffy, about 2 minutes. Turn the mixer to low and add the egg, mixing until incorporated. Scrape down the bowl and paddle as needed.
Add the vanilla and sour cream, then turn the mixer to high and beat for 1 minute. Meanwhile, mix the strawberry purèe into the whole milk and set aside.
Turn the mixer off and add all of the dry ingredients at once. Mix on low speed until just combined, then add the strawberry milk mixture and pink food coloring (if using) until just combined, about 30 seconds. Give the batter a few stirs by hand to make sure everything is incorporated without over-mixing.
Pour the batter evenly between the prepared cake 4-inch pans (or all into one 6-inch cake pan). If using 4-inch cake pans, bake for 18-22 minutes. If using a 6-inch cake pan bake for 24-28 minutes. The cake is done when it springs back to the touch and a toothpick inserted comes out clean. Cool completely before assembling and decorating.