Add butter to a medium saucepan or skillet. Place over medium heat and cook, stirring constantly, until the butter melts, starts to sizzle and simmer, and eventually browns. This whole process will take about 5 minutes. The butter will foam and sizzle quite a bit in the early stages but will eventually calm down as it gets closer to browning. As soon as the butter has browned, pour it into a large bowl - make sure to scrape in those brown bits from the bottom of the pan! Take care not to let the butter sit for too long in the pan after browning or the residual heat can burn it!
Set the brown butter aside to cool completely to room temperature but do not let it solidify. It'll take about 20 minutes to cool (depending on how cold / warm your home is).
In a separate medium bowl, whisk together flour, baking soda, baking powder, cinnamon, and salt. Set aside.
Now back to the cooled brown butter, add brown sugar to the bowl and whisk to combine. The mixture will be a bit grainy.
Add maple syrup, egg, and vanilla and whisk until smooth. Fold in the flour mixture until you have a streak free cookie dough.
The cookie dough should be able to hold a scoop shape - if it's a little soft, let it sit at room temperature for about 10 minutes to firm up. Use a large cookie scoop to portion out 4 or 5 balls of cookie dough onto one parchment lined baking sheet, leaving at least 3 inches of space between each cookie.
Bake the cookies, one baking sheet at a time, in the center of your preheated oven for 10 to 12 minutes or until golden brown along the edges and the center no longer appears raw.
Cool the cookies for about 5 minutes on the baking sheets then transfer onto a wire rack and set aside to cool completely. Continue baking the rest of the cookie dough in batches.
In a medium sized bowl or measuring cup, combine powdered sugar, salt, and maple syrup. Whisk together until smooth and pourable. If the icing is too thick, you can thin it out with a splash of water. If it's too thin, whisk in more powdered sugar to reach your desired consistency.
Drizzle the salted maple icing over the cooled cookies and top with sea salt flakes if using. Enjoy!
