Preheat your oven to 350°F (175°C) and line your baking sheet with parchment paper.

In a medium saucepan, melt the salted butter over medium heat, stirring until golden brown, about 5-8 minutes.

Combine the cooled brown butter with dark brown sugar, eggs, and vanilla bean paste in a mixing bowl. Beat until smooth.

In another bowl, whisk together flour, oats, baking soda, espresso powder, cinnamon, and kosher salt. Add to wet ingredients and mix gently.

Cover the dough with plastic wrap and chill in the refrigerator for 30 minutes.

Scoop the chilled dough onto the baking sheet, spacing about 2 inches apart.

Bake for 10-12 minutes until the edges are barely golden. Let them cool on the sheet for 5 minutes.

In a bowl, whisk together any reserved brown butter, powdered sugar, espresso powder, vanilla, and milk until smooth.

Dip the tops of cooled cookies into the icing and allow to set on parchment paper.