Sift flour and salt into a medium bowl; set aside. Put butter and sugar into the bowl of an electric mixer fitted with the paddle attachment, and mix on medium speed until pale and fluffy, 2 to 3 minutes, scraping down sides of bowl as needed. Reduce speed to low. Mix in egg yolk and vanilla bean or extract. Gradually add flour mixture; mix until just combined, about 1 minute.
Remove half of the dough; set aside. Add cocoa powder and chopped chocolate to remaining dough; mix on low speed until well combined. Turn out chocolate dough onto a lightly floured work surface. Roll into a 10-inch log, about 1-inch wide and 1/2-inch tall. Repeat with reserved vanilla dough. Wrap each rectangle in plastic wrap, and refrigerate until slightly firm, at least 30 minutes.
Remove the chilled doughs from the fridge. Brush the top of the chocolate piece with a bit of a remaining egg white. This will help the chocolate and vanilla stick together. Press the vanilla piece on top of the moistened chocolate piece. Press lightly. Rewrap dough and refrigerate for at least 2 hours, or overnight.
Preheat oven to 350 degrees. Cut log into 1/4-inch-thick rounds; space 1 inch apart on baking sheets lined with parchment paper. If dough becomes too soft to slice cleanly, return to freezer until firm. Sprinkle course sea salt onto the chocolate half of the cookies. Press in lightly with fingertips.
Bake until firm to the touch, 10 to 12 minutes. Transfer to wire racks; let cool. Cookies can be stored in airtight containers at room temperature up to 3 days.