In a skillet over medium heat, melt salted butter while stirring constantly for about 3–4 minutes until it turns a golden brown.

In a large mixing bowl, whisk together the warm browned butter, brown sugar, pumpkin butter, egg, vanilla extract, and espresso powder until smooth.

In a separate bowl, sift together flour, rolled oats, baking soda, pumpkin pie spice, and salt.

Carefully fold the dry ingredients into the wet mixture until no streaks of flour remain.

Using a tablespoon, scoop the dough, roll into balls, and slightly flatten each ball before placing on a lined baking sheet.

Preheat your oven to 350°F (175°C) and bake the cookies for 8 minutes, rotating the pan halfway through.

Let the cookies cool on the baking sheet for about 5 minutes before preparing the icing.

In a small saucepan, brown additional salted butter and whisk with powdered sugar, vanilla extract, and a pinch of salt.

Spread the brown butter icing over each cooled cookie while it's still soft.