Make dough in a food processor:
In a food processor, combine the sugars, salt, and 1 1/2 cups (195 grams) of flour in the work bowl to make the dough. Mix or pulse in the cold, diced butter until it disappears, then continue to run the machine until it just begins to clump. Add the egg yolk and vanilla extract and pulse until combined, then continue to run the machine until one large or a few smaller smooth masses form.
In the work bowl, combine the sugars, salt, and 1 1/2 cups (195 grams) of flour. Add cold, diced butter, and mix or pulse until it disappears, then continue to run the machine until it just starts to clump. Add the egg yolk (reserve the whole egg). (reserve the egg white for later) and vanilla and pulse until combined, then continue to run the machine until one large or several smaller smooth masses form.
Make dough in a stand mixer or with a hand mixer:
In the bowl of your stand mixer, cream together the butter, sugars, and salt until creamy. If you started with cold butter in a stand mixer, this will take a few minutes and a few scrapes down the bowl.
When the mixture is thoroughly combined, add the egg yolk (reserve the egg white for later) and vanilla extract and beat until combined.1 1/2 cups (195 grams) flour, beaten until it disappears into a smooth dough
Both methods:
Cut the dough in half.[Each half will weigh between 270 and 275 grams.]One-half should be left in the mixing bowl or food processor. Add the remaining 1/4 cup (35 grams) flour and pulse/mix until just combined. Scrape the vanilla dough out of the mixing bowl or food processor and set it aside. Add the cocoa powder to the second half of the dough in the mixing bowl or food processor.
Mix until everything is well combined. This is your chocolate dough at this point.
Heat oven: To 350°F (176°C)
To checkerboard the doughs:
- Place each dough half between two pieces of parchment paper and roll each into (approximately) 4 to 5×10-inch (10 to 13×25-cm) rectangles that are 1/4-inch (6mm) thick. Slide both slabs of dough onto a cutting board or tray and freeze for 10 to 15 minutes, until firm like cold butter but not quite frozen solid.
- Remove the top piece of parchment from each slab (you can use these to line your baking sheet) and stack the chocolate and vanilla dough layers, pressing them gently together. Cut the slab in half the long way (i.e. forming two approximately 2×10-inch rectangles) and stack the halves, forming one long, striped slab. Press the layers gently, to adhere them, and return this to the freezer for another 10 to 15 minutes, or until it’s very firm but not fully frozen.
- Remove this long slab from the freezer and, using your sharpest knife and steadiest hand, cut it the long way into eight 1/4-inch-wide slices. Arrange the first four into a checkerboarded log, flipping two of the slices over so the opposite flavor is on top. Repeat with the second four into a second checkerboarded log. Wrap each in a piece of parchment paper and press it firmly into a long, squared-off log, adhering the layers. Return to the freezer for one last 10-minute stint, until solid to the touch.
To finish cookies:
Line a large baking sheet with parchment paper, or discarded parchment from your cookie slabs. Beat reserved egg white until just loosened. Gather your sanding sugar(s).
Unwrap the first checkered log. Roll or sprinkle sanding sugar on top of the egg white-brushed log.
[Typically, people select one color per log.[I divided each log into quarters and painted each quarter a different color.]Slice the sugar-coated log into 1/4-inch thick cookies and place them on a baking sheet with a 1-inch gap between them (they expand slightly). Rep with the second log, making more cookies.
Bake cookies:
For 10 to 12 minutes, or until golden brown underneath. Let cookies rest on the tray for 5 minutes, so they firm up a little, before transferring to a cooling rack to finish cooling and crisping up.
Do ahead:
Baked, cooled cookies keep for 3 weeks in a tin at room temperature.
To spiral the doughs:
Roll your chocolate and vanilla dough slabs to 1/8-inch thickness and stack them, gently patting them together.
Chill for 5 to 10 minutes in the freezer, or until cold but not hard. Divide the dough into two equal-length pieces. Roll each half of the dough into a tight spiral, with the vanilla dough underneath/forming the outer ring.[I forgot and did the opposite, but I always think vanilla on the outside looks better.]Wrap each spiral in parchment paper and roll the dough into a tight log.
Chill in the freezer for 15 minutes, or until solid but not hard. Continue with the instructions from “To finish cookies:” above.
To marble the doughs:
Roll your chocolate and vanilla dough slabs to 1/8-inch thickness and stack them, gently patting them together. Cut the log into two stacked sections, squeeze each into a rough log, fold it over, and mash it, kneading it once or twice. Form kneaded mounds into a long log shape by pressing them together. Wrap the dough in parchment, pressing it into a firm log. Chill in the freezer for 15 minutes, or until solid but not hard. Continue with the instructions from “To finish cookies:” above.
