Position oven racks in top and bottom thirds of oven. Preheat oven to 275°F. Line 2 baking sheets with parchment paper.
Use an electric mixer to whip egg whites until foamy. With mixer still running, add sugar in a slow, steady stream. Continue to beat until whites are shiny and stiff.
Sift cocoa and espresso powder over whites. Add vanilla. Gently fold into egg whites.
Pipe or drop heaping tablespoonfuls onto prepared baking sheets, leaving 1 1/2 inches between cookies. Bake until firm on outside, 30 to 35 minutes. Cool completely on baking sheets. Peel kisses off paper and store in an airtight container for up to 2 days.