Step 1
Preheat the oven to 325 degrees F (165 degrees C) with racks in the upper and lower third. Line 2 large baking sheets with parchment paper.
Step 2
Whisk flour sugar and baking soda together in a large bowl. Set aside.
Step 3
Beat butter using the paddle attachment of an electric mixer on medium-high speed until fluffy about 1 1/2 minutes. Gradually add flour mixture and beat on medium-low speed until just combined about 2 minutes. Divide dough into quarters.
Step 4
Working with one quarter at a time roll dough between 2 large sheets of parchment until 1/8-inch thick. Chill between the parchment on a baking sheet until firm about 15 minutes.
Step 5
Cut out enough cookies to fill the 2 baking sheets with 2-by-1 1/2-inch rectangles or your desired shapes. Arrange 1 inch apart on the sheets. Brush tops of cookies with some of the egg and sprinkle evenly with a portion of turbinado sugar. Keep unused dough in the fridge.
Step 6
Bake cookies 2 sheets at a time until pale golden 14 to 15 minutes rotating pans after 7 minutes. Let cookies cool on sheets for about 5 minutes then carefully move them to a wire rack to cool completely before dipping. Cut brush and bake the remaining cookie dough in the meantime.
Step 7
Place chocolate in a microwave-safe bowl. Microwave on high for 30-second intervals until melted and smooth about 1 1/2 minutes. Either dip cookies halfway in chocolate mixture and let excess drip off or use a fork and drizzle chocolate Jackson Pollack-style over cookies over a parchment-lined baking sheet. Sprinkle salt over chocolate. Let rest until chocolate sets about 1 hour.