In the bowl of a food processor fitted with a blade, pulverize the strawberries into a powder. (You can sift the seeds out if desired, but don't need to).
In the bowl of a stand mixer fitted with a paddle, beat the butter on medium speed until creamy, about 1 minute. Add the granulated and confectioners' sugar and salt, and beat again on medium speed until light and fluffy, 2 to 3 minutes. Scrape down the bowl and add the egg yolks and vanilla, and mix on low speed until incorporated. Then add the flour and mix on low speed until just combined.
Dump the dough out onto a work surface and divide it into three equal portions. Put one-third of the dough back into the mixer and add the powdered strawberries and food coloring, if using. Mix on low speed until totally combined, then remove the dough.
Add another third of dough to the mixer. Add the cocoa powder and mix on low speed until totally combined. If the cocoa powder is not incorporating quickly, add the teaspoon of water to the mixing bowl.
Divide each of the three flavor portions of dough into two equal pieces, for six pieces of dough total. Stack one chocolate, one strawberry, and one vanilla on top of each other, and gently press the pieces together. Pat and form into a log, about 2 in [5 cm] wide and 8 in [20 cm] long. Place the log on a large piece of plastic, a few inches longer than the log. Sprinkle about a teaspoon of sanding sugar over each side of the log, covering the outside of the dough. Gently press the sugar into the dough with your hands. Wrap the log in the plastic wrap and refrigerate until firm, about 2 hours, or overnight. Repeat with the remaining dough.
When ready to bake, adjust an oven rack to the middle of the oven. Preheat the oven to 350F [180C]. Line two sheet pans with parchment paper.
Sprinkle some more sanding sugar over each side of the log, if desired. Slice the chilled log into ½ in [12 mm] thick pieces (you can go up to 3/4 in if you want them a little thicker). Space the pieces about 2 in [5 cm] apart on the sheet pans. Bake one pan at a time, rotating halfway through baking. Bake until the edges are light golden brown but the centers are still pale, 13 to 15 minutes. Move the pan to a wire rack and let the cookies cool completely on the pan. Store cookies in an airtight container at room temperature for up to 3 days.