Preheat oven to 350°F. Grease an 8x8 inch pan. If desired, line with parchment paper or foil.
In a medium bowl whisk together sugar, melted butter, and cocoa until well combines, 2 to 3 minutes.
Add eggs, one at a time, stirring until incorporated, then add vanilla.
In a small bowl dissolve espresso powder in the water. Add to batter, whisking until combined.
Using a wooden spoon or rubber spatula, gently fold flour into batter until combined. (Avoid overmixing; batter should be smooth and fluffy.) Gently fold in any stir-ins (if using).
Spoon batter into prepared pan, spreading evenly. Bake until center is just set, 20 to 22 minutes. (Do not over bake.)
Let cool at least 10 minutes before cutting into squares.