In a food processor, add the sugar and strawberries and pulse until mixture turns to a reddish/pinkish powder.
Transfer the strawberry sugar to the bowl of a stand-up mixer with the paddle attachment.
Add the butter, vanilla extract and salt. Beat until the mixture is light and fluffy and turns a pale pink, 2 to 3 minutes.
Add the flour, in two batches, and mix until combined. Remove half of the dough and place on a sheet of plastic wrap.
To the stand-up mixer with the remaining dough, add the cocoa powder and mix until thoroughly combined.
Wrap the two doughs in plastic wrap, separately, and transfer to the fridge for 15 minutes.
Roll out each dough so it’s a 7-inch square that’s 1/2-inch thick. Slice each square into 1/2-inch wide strips.
Handling the strips delicately, place the logs, alternating between colors, next to one another. Brush the top lightly with the beaten egg.
Repeat with the next layer, starting with the opposite color and alternating between colors. Repeat this process until you have 5 layers.
Wrap the square log with plastic wrap and transfer to the freezer to chill for 10 minutes.
Preheat the oven to 350 F and line a baking sheet with parchment. Slice the logs into 1/4-inch to 1/2-inch thick cookies.
Place on the baking sheet and bake for 10 to 12 minutes. Allow to cool completely on the baking sheet before moving them.
