Place the butter in a saucepan over medium heat and cook until it turns golden brown and smells nutty. Pour it into a mixing bowl and let it cool for 5 minutes.

Add the granulated sugar, egg, and 1 teaspoon of the vanilla extract to the cooled brown butter. Stir until smooth.

In a separate bowl, whisk together the flour, baking soda, and salt. Gradually mix the dry ingredients into the wet mixture until a dough forms.

Scoop the dough into 12 portions and place them on a baking sheet lined with parchment paper. Flatten each slightly with your hand.

Bake at 350°F for 10 to 12 minutes until the edges turn light golden. Remove from the oven and let the cookies cool completely on the sheet.

While the cookies cool, stir together the powdered sugar, milk, and remaining teaspoon of vanilla extract until the icing reaches a thick but pipeable consistency.

Transfer the icing to a piping bag fitted with a small round tip. Pipe bone shapes onto each cooled cookie and let the icing set for 30 minutes.