Combine the dry ingredients, flour, baking soda, and salt in a large mixing bowl. Whisk them together thoroughly and set the bowl aside.
In another bowl, blend the wet ingredients, sourdough starter, melted butter, brown sugar, maple syrup, maple extract, and egg until smooth and creamy.
Transfer the wet ingredients to the bowl containing the dry ingredients. Use a spatula or wooden spoon to carefully blend all the ingredients. (Make sure the dough is smooth and not sticky. If it's sticky, mix in 2-3 tablespoons of flour.)
When you're ready to bake, place the oven rack in the center position and preheat your oven to 350°F (176°C). Line a baking sheet with parchment paper or a silicone mat.
Use a 2-tablespoon cookie scoop to portion out 12 cookie dough balls on a baking sheet lined with parchment paper. Bake the cookies for 11-13 minutes until they spread and the tops begin to crack. Transfer the cookies to a wire rack to cool.
Mix 1 tablespoon of melted butter with the maple syrup and powdered sugar until smooth. Transfer the glaze to a ziplock bag, snip off the edge of the bag, and drizzle the glaze in a zig-zag motion over each cookie. Sprinkle a little granulated sugar if desired.