To make the cookies, heat the oven to 350°F with racks in the upper- and lower-middle positions. Line 2 rimmed baking sheets with kitchen parchment. In a medium bowl, whisk together the flour, cinnamon, ginger, baking powder and baking soda; set aside.

In a large bowl, combine the molasses, brown sugar and melted butter. Whisk to combine, then whisk in the buttermilk. Add the eggs and whisk until smooth. Add the flour mixture and fold with a silicone spatula just until no streaks of flour remain; the dough will be thick.

Using a ¼-cup dry measuring cup or a 1½-inch ice-cream scoop, drop scant ¼-cup mounds of dough onto the prepared baking sheets, arranging them in 3 rows of 3 and spacing them evenly.

Bake until the cookies are domed and a toothpick inserted at the center comes out clean, 12 to 15 minutes, switching and rotating the baking sheets about halfway through.

Cool completely on the the baking sheets on wire racks, about 30 minutes. Using a metal spatula, transfer the cookies directly to the racks.

To make the icing, in a 10-inch skillet over medium-high, melt the butter. Cook, swirling the pan frequently, until the milk solids at the bottom are golden brown and the butter has a nutty aroma, 1 to 3 minutes. Transfer to a medium bowl.

Whisk in the powdered sugar, buttermilk and vanilla until smooth. The icing should have the consistency of smooth peanut butter; if it is too thick, whisk in additional buttermilk 1 teaspoon at a time until spreadable.

Using the back of a spoon or a small spatula, spread 1 tablespoon of icing evenly onto each cookie. Let the icing dry for about 30 minutes before serving.