Beat the butter, maple sugar, salt, and vanilla in a medium bowl with an electric mixer until smooth and creamy, about 1 minute. Add the pecans and flour and mix until just incorporated. If there are any dry bits simply stir them into the batter with a spoon or knead the dough with your hands. Form the dough into a 12 x 2-inch log. Wrap tightly with plastic wrap and refrigerate for 2 hours.
Preheat the oven to 350ºF and adjust racks to the upper and lower thirds of the oven. Line two baking sheets with parchment paper. Unwrap the dough and using a sharp knife, cut the dough into 1/4-inch slices. Place the cookies 1 1/2 inches apart on the baking sheet. Bake for 12 minutes rotating pans half-way through baking, until the edges are just golden brown. Cool completely.
Dip each cookie in the melted chocolate and place on a cooling rack to dry. Serve when chocolate is set, about 1 hour.