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Step 1
Prep: Spray or line a large baking sheet and set aside. Prepare the flax “egg” by mixing the flaxseed and water well; set aside for at least 5 minutes to let thicken.
Step 2
Brown the Butter: Add the butter to a small pan or pot and warm over medium heat, stirring occasionally. The butter will melt completely, then begin to bubble as a white “foam” rises to the top of the butter. Start to stir frequently now, until the foam darkens in color and the protein solids fall to the bottom of the pan and turn golden; this process should take around 10 minutes in total. Remove the butter from the heat immediately and transfer to a glass measuring cup (scrape the pan well!). Place the cup in the fridge for 10 minutes, to allow the butter to cool.
Step 3
Dry Ingredients: In the meantime, whisk the flour, cornstarch, cinnamon, baking soda, and salt together in a bowl. Set aside.
Step 4
Wet Ingredients: In a separate bowl whisk the brown sugar and chilled brown butter together until combined. Add in the flax egg, maple syrup, vanilla extract, and maple extract (if using) and mix again. Transfer the wet ingredients to the dry and mix until a dough forms.
Step 5
Chill: Cover the dough with plastic wrap and refrigerate for at least one hour. This will allow the butter to re-solidify and for the flour to absorb more moisture and flavor.
Step 6
Preheat the oven: Preheat the oven to 350F while the cookie dough chills.
Step 7
Roll: Mix the cane sugar and the cinnamon together in a small bowl and set aside. Form 2-tablespoon balls of cookie dough, rolling it smooth between your hands. Roll each cookie dough ball in the cinnamon sugar, then place each cookie 2” apart on the baking sheet.
Step 8
Bake: Bake in the middle rack of the oven for 10 to 12 minutes; the cookies will look puffy and pale, but the bottom edges should be golden. Let the cookies rest on the baking sheet for another 10 minutes, where they will deflate fully. Transfer to a wire rack and let cool completely.
Step 9
Make the Maple Glaze: Add the melted butter to a small bowl along with the maple syrup and 1/2 cup of the powdered sugar. Whisk well, until a smooth icing form; if the mixture is too thin, add additional powdered sugar in 1 tablespoon increments. You can transfer the icing to a piping bag if you want your cookies to be decorated neatly, or simply use a spoon to drizzle the icing over the cooled cookies for a more rustic feel.
Step 10
Serve & Store: Serve cookies after drizzling, or allow the frosting to fully set and harden before storing. Store cookies in an airtight container at room temperature for up to 4 days. Cookies can also be stored in the freezer for up to one month and reheated as necessary.