Mix the flour, soda, and salt in a bowl and set asidde
In a food processor/chopper grind the strawberries to a powder. I suppose you could do this with a mortar-and-pestle or a rolling pin, too. My chopper is particularly awful so I always have to mortar up some of them.
In a stand mixer fitted with the paddle beat the butter until creamy. Scrape down the sides.
Add the sugar and beat until light and fluffy. A couple of minutes. Scrape down the sides.
Add the egg, egg yolk, and vanilla and beat until combined, scraping down the sides as necessary.
Add the flour a bit at a time and beat on low speed until combined. If your mixer is like mine, you'll need to scrape it down a few times.
Dump the dough out of your mixer and weigh. Should be around 1000 grams but could be more or less. Divide into 3 equal portions. (And you thought you'd never need math after you left school!)
Put one chunk aside. That's your "white" section.
Put one chunk in the mixer and, on low, add the powdered strawberries and, if using, the food coloring. (The pulverized strawberries won't make it very red; thus the food coloring.)
Remove the strawberry dough from the mixer, wipe out the mixer and wipe off the paddle. Then add another dough portion to the mixer and mix slowly with the cocoa powder until well blended and even colored.
Heat oven to 350°F / 175°C