Heat the oven to 350°F and line two baking sheets with parchment. Whisk the melted butter, granulated sugar, brown sugar, molasses and egg yolk until smooth.
Whisk flour, ginger, cinnamon, baking soda and salt, then stir into the butter mixture just until combined.
Divide into 24 small portions, roll into balls and flatten to 1/4-inch-thick discs on the sheets, leaving 2 inches between them. Sprinkle with coarse sugar.
Bake one sheet at a time for 11 to 12 minutes, until the surfaces are cracked and the centers look dry rather than glossy.
Let stand on the sheets for 5 minutes, then cool fully on racks; the cookies become crisp as they cool.