Line an 8-inch square baking pan with parchment paper, leaving a 2-inch overhang on all sides. Spray parchment with nonstick cooking spray.
Combine the condensed milk, sugar, and butter in a large saucepan over medium/low heat. Stirring frequently, bring to a low boil. Stir in chocolate chips and espresso powder. Stop stirring and let boil undisturbed for about 8 minutes. (If using a candy thermometer, the temperature should read 235°F.)
Carefully remove pan from the heat and stir in vanilla extract. Let mixture cool for 10 minutes. (A skin may begin to form on the surface; this is fine.) Using an electric mixer, beat mixture on medium/high for 5 minutes, until it is the consistency of soft peanut butter. Scrape mixture into the prepared pan and smooth to the edges. Chill until firm, about 4 hours.
Run a knife around the edges of the pan to loosen the fudge. Using the parchment overhang, lift the fudge out of the pan. Cut into 1½-inch squares. Keep refrigerated, in an airtight container, for 2 weeks.