In a large bowl, whisk together the flour, baking soda, and salt; set aside.
Using an electric mixer, beat the butter and sugar until smooth. One at a time, beat in 2 of the eggs; beat until fluffy, about 2 minutes. Mix in the vanilla extract.
With the mixer on low, gradually add the flour mixture, mixing until just incorporated (the dough will be stiff). Shape into 2 disks and refrigerate, wrapped, for at least 1 hour and up to 3 days.
Heat oven to 350° F. On a floured surface, roll pieces of the dough into ⅜ -inch-thick cords and cut into 6-inch lengths. Shape into twists, then place on parchment-lined baking sheets.
Beat the remaining egg. Brush the twists with the beaten egg and sprinkle with the coarse sanding sugar.
Bake until just beginning to brown, 15 to 18 minutes. Cool slightly on baking sheets, then transfer to wire racks to cool completely.
Keep at room temperature in an airtight container for up to 1 week.
