Melt butter in a medium saucepan over medium heat. Let cool 10 minutes. Pour through a fine sieve into a clean pan.Advertisement
Return to heat. Add sugar; whisk until sugar has dissolved. Bring to a simmer; cook 1 minute. Whisk in espresso.
Pour through a fine sieve into a medium bowl; let cool until slightly thickened, 5 to 7 minutes. Whisk before using.