Combine flour, 1 cup sugar, cocoa, chicory, and baking powder in the bowl of a mixer. Add butter and beat on medium speed until sandy, about 3 minutes. Reduce speed to low, and gradually beat in eggs and 1 egg yolk. Add chocolate chips and mix until just combined.
Divide dough in half and roll each half into a 1 1/2-inch-thick log (about 12 inches long) on a lightly floured surface. Wrap each log in plastic wrap. Refrigerate for at least 1 hour.
Preheat oven to 325 degrees. Unwrap logs; transfer to a parchment-lined baking sheet. Whisk together remaining egg yolk and cream. Brush tops of logs with egg wash and sprinkle with remaining tablespoon sugar. Bake until firm, about 35 minutes.
Transfer logs to a wire rack and let cool completely. Cut each into 1 1/4-inch-wide wedges with a serrated knife by alternating the angle of the knife as you slice crosswise.
Unbaked dough logs can be refrigerated for up to 1 week or frozen for up to 1 month. Thaw before baking. Cookies can be stored at room temperature for up to 1 week.