Preheat the oven to 350℉. Line a baking sheet with parchment paper and set aside.
Brown the Butter: Cut the two sticks of butter into tablespoon-sized cubes. Add the cubed butter to a medium-sized saucepan and bake on medium heat over the stove. Stir continuously as the butter melts and starts to brown. Be careful not to burn it! The butter is ready when it is brown in color and there is foam on top, about 5-7 minutes. Remove from heat and let it cool before making the cookie dough.
Pro Tip: Set the saucepan in a bowl of ice (make sure to use a glass or stainless steel bowl for this because plastic bowls can melt from the hot saucepan) to help cool down the browned butter faster.
Add the browned butter to a large mixing bowl. Make sure to scrape it all in there--especially the sediments you see at the bottom of the pan! If your brown butter sat a little too long on the bowl of ice, that's just fine--scrape the solidified brown butter into the bowl.
Make the Cookie Dough: Next, add the brown sugar and maple syrup to the bowl and cream the ingredients together for a minute or two on medium speed with a mixer.
Add the eggs one at a time as you mix the ingredients. Add the vanilla extract and sourdough discard.
Sift together the baking soda, salt, and flour in a medium-sized mixing bowl. Gradually add the dry ingredients to the bowl of wet ingredients, mixing until just combined. Make sure to scrape the sides of the bowl with a rubber spatula to incorporate all the flour.
Scoop the Cookie Dough: Use a spoon or 2-teaspoon-sized cookie scoop to scoop the cookie dough balls onto the baking sheet. Space each cookie dough ball about 2 inches apart to allow them to rise as they bake.
Bake the Cookies: Bake for about 9 minutes, or until the edges are golden brown but the center of the cookies are still soft and slightly undercooked. Allow the cookies to cool on the pan for about 5 minutes before transferring to further cool on a wire race. The recipe makes about 24 cookies.
Make the Maple Icing: In a medium-sized mixing bowl, whisk together the powdered sugar, maple syrup, and melted butter. Drizzle over the cookies. Let the icing harden before serving. Enjoy!