Step 1

Begin by browning the butter. Place the butter in a saucepan set over medium-low heat. Cook, stirring occasionally, until light brown bits form on the bottom of the pan and the butter begins to turn golden and smell nutty. Watch it closely as it can go from brown to burned quickly. Immediately transfer the butter into a bowl along with any accumulated brown bits. Allow the butter to cool at room temperature for 30 minutes.

Step 2

Preheat oven to 350°F. Line two baking sheets with parchment paper.

Step 3

Remove 1½ tablespoons of the brown butter (including some of the bits at the bottom of the bowl) and set it aside; it will be for the icing.

Step 4

Using a hand mixer or stand mixer fitted with the paddle attachment, beat the remaining brown butter, brown sugar, and granulated sugar. Add egg and vanilla, beating until combined.

Step 5

In a separate bowl, combine flour, baking soda, salt, and cornstarch. Add to the sugar mixture and beat until well combined.

Step 6

Scoop the dough into 1½ - 2 tablespoon portions and place a couple inches apart on the parchment lined baking sheets. Be sure that the dough balls are mounded, not flattened, so that they bake up with a nice thickness.

Step 7

Bake for 8-10 minutes, until the edges are beginning to set but the centers are still slightly under baked. Place the baking sheets on wire racks to cool completely (see note about shaping cookies). Once cool, proceed with the icing.

Step 8

If the reserved 1½ tablespoons of brown butter has solidified you can microwave it for a few seconds, until melted. Whisk the melted brown butter and all remaining icing ingredients until smooth. Adjust the consistency by adding more milk to thin or more powdered sugar to thicken. Drizzle the icing over the top of each cookie (I use a ziptop bag with the corner snipped off). Immediately sprinkle with flaky sea salt.