Using an electric mixer on medium speed, beat the butter, sugar, brown sugar, and vanilla until fluffy.
Reduce mixer speed to low. Add the flour and salt, mixing just until combined. Stir in the chocolate.
The dough will be crumbly but should hold together when pinched. If the dough is not holding together, continue mixing and (only if necessary) mix in 1 tablespoon water.
Form the dough into 2 balls and flatten into discs. Wrap each disc tightly in plastic wrap. Refrigerate for 1 hour.
Preheat oven to 325°F (160°C). Line baking sheets with parchment paper or silicone liners.
On a lightly floured surface, roll out 1 disc of dough to about 1/4-inch thickness. Cut the dough into 1"x 2" strips. Carefully transfer the cookies to the prepared baking sheet. Sprinkle with coarse salt.
Bake 18-22 minutes, or until the cookies are lightly browned. Cool on the pans for 10 minutes. Then, transfer the cookies to wire racks to cool completely.
Repeat the rolling and baking process with the other disc of dough.