Pumpkin Cookies with Brown Butter Icing

I'm not sure what is a better description of these cookies... cookies, or cupcake tops (which reminds me of the Seinfeld episode about the Muffin Tops- it's a classic, you should watch it).
These are soft, cakey circles of delicious pumpkiny goodness, and the brown butter icing tops them off perfectly. One batch makes a TON of cookies. I made 50 cookies, and still had leftover batter.

Pumpkin Cookies with Brown Butter Icing

Credit: Martha Stewart Living, October 2004

Ingredients:

For the Cookies-

2 ¾ cups all-purpose flour
1 teaspoon baking powder
1 teaspoon baking soda
1 ¼ teaspoons coarse salt
1 ½ teaspoons ground cinnamon
1 ¼ teaspoons ground ginger
¾ teaspoon ground nutmeg
¾ cup (1 ½ sticks) unsalted butter, softened
2 ¼ cups packed light-brown sugar
2 large eggs
1 ½ cups canned solid-pack pumpkin (14 ounces)
¾ cup evaporated milk
1 teaspoon pure vanilla extract

For the Icing-

4 cups confectioners' sugar, sifted

10 tablespoons (1 ¼ sticks) unsalted butter

¼ cup plus 1 tablespoon evaporated milk

2 teaspoons pure vanilla extract

Directions:

1. Make cookies: Preheat the oven to 375 degrees. Whisk together flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg in a medium bowl; set aside.
2. Put butter and brown sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until pale and fluffy, about 3 minutes. Mix in eggs. Reduce speed to low. Add pumpkin, evaporated milk, and vanilla; mix until well blended, about 2 minutes. Add flour mixture; mix until combined.
3. Transfer 1 ½ cups batter to a pastry bag fitted with a ½-inch plain tip (or you can just cut the corner off from a ziplock bag-  works fine, you just won't have as perfect of circles). Pipe 1 ½-inch rounds onto parchment-lined baking sheets, spacing 1 inch apart. Bake cookies, rotating sheets halfway through, until tops spring back, about 12 minutes. Cool on sheets on wire racks 5 minutes. Transfer cookies to wire racks; let cool completely.

4.   Make icing: Put confectioners' sugar in a large bowl; set aside. Melt butter in a small saucepan over medium heat. Cook, swirling pan occasionally, until golden brown, about 3 minutes. Immediately add butter to confectioners' sugar, scraping any browned bits from sides and bottom of pan. Add evaporated milk and vanilla; stir until smooth. Spread about 1 teaspoon icing onto each cookie. If icing stiffens, stir in more evaporated milk, a little at a time.