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

Stir the flour, granulated sugar, vanilla extract, and salt into the cooled brown butter until a dough forms. Shape the dough into a disk, wrap it, and chill for 20 minutes.

Heat the oven to 350 degrees and line a baking sheet with parchment. Roll the dough to 1/4-inch thickness and cut out 3-inch circles. Place them on the sheet and bake for 12 to 14 minutes until the edges are lightly golden.

Cool the cookies completely on a wire rack. Mix the powdered sugar with milk until smooth, then divide the icing into two bowls. Tint one bowl orange and the other black.

Spread orange icing over each cookie. Once set, pipe black icing to draw jack-o'-lantern faces on top.