Prep the basics: Line two baking sheets with parchment.
Set butter and eggs out to reach room temperature. Preheat oven to 350°F (177°C) when ready to bake.
Whisk dry ingredients: In a bowl, whisk flour, baking powder, baking soda, and salt until evenly combined.
Cream the butter and sugars: In a large bowl, beat butter, granulated sugar, and brown sugar until light and fluffy, about 2–3 minutes. Scrape the bowl as needed.
Add eggs and vanilla: Beat in the egg and egg yolk one at a time, then mix in vanilla.
Blend until smooth and glossy.
Bring in the dry mix: Add the flour mixture in two additions. Mix on low just until no dry streaks remain. Do not overmix.
Split the dough: Divide the dough in half.
To one half, add cocoa powder and 1 tablespoon milk (and espresso powder if using). To the vanilla half, add 1 tablespoon milk to keep textures even. Mix each half until smooth.
Create woodgrain swirls: On a lightly floured surface, press each dough half into a rectangle (about 8x5 inches).
Tear or cut each rectangle into 4–5 rough strips. Stack and alternate chocolate and vanilla strips, pressing lightly so they stick but keep some seams visible.
Form logs: Gently roll the stacked dough into a log about 2 inches in diameter. Don’t overwork—irregular swirls create the wood look.
If using the “bark” edge, roll the log in mini chocolate chips or chopped chocolate to coat the outside.
Chill: Wrap logs tightly in plastic and chill for at least 2 hours, or freeze for 30–45 minutes until firm. Well-chilled dough slices cleanly and holds the pattern.
Slice: Using a sharp knife, slice 1/4-inch rounds. If edges crack, nudge them back into shape.
Place 2 inches apart on prepared sheets.
Bake: Bake 9–12 minutes, until edges are set and just turning golden. The centers should look slightly soft. Rotate pans halfway for even baking.
Cool: Let cookies rest on the sheet for 5 minutes, then move to a wire rack to finish cooling.
The pattern becomes more defined as they set.