Preheat the oven to 350 degrees F (175 degrees C). Grease two cookie sheets.
Sift flour, baking soda, and salt into a bowl.
Cream butter and brown sugar in a large bowl with an electric mixer. Mix in maple syrup, egg, and vanilla until well blended. Mix in flour mixture until well blended.
Shape dough into 1-inch balls. Fill two cookie sheets with balls, 2 inches apart. Flatten slightly with the bottom of a glass. Sprinkle each cookie with some of the remaining sugar.
Bake in the preheated oven until golden, 8 to 10 minutes. Transfer to wire racks to cool. Repeat to bake remaining cookies.
