Add the butter to a medium nonstick saucepan over medium-high heat. Cook, stirring occasionally, until the butter turns dark brown and smells nutty. Watch carefully so the butter does not burn. Remove the pot from the heat. Add an ice cube to the butter and slowly let it melt. It may froth and bubble. Add the remaining 3 ice cubes and gently stir until melted. In a large bowl, combine the granulated and brown sugar, espresso powder, salt, and baking soda. Pour the brown butter into the sugar mixture and mix until combined. Don’t worry if it looks separated. In a small bowl, whisk together the eggs and vanilla. Pour into the sugar and butter mixture and whisk until glossy and smooth. Add the flour and fold with a rubber spatula to incorporate until the dough has no visible flour streaks.