Preheat your oven to 350°F.
Butter and line a 9-by-13-inch metal baking dish with parchment paper.
In a small saucepan, melt the butter over low heat, then add the chocolate. If needed, heat the mixture for an extra 10 seconds until fully melted.
Set aside the chocolate mixture to cool.
Sift the flour, espresso powder, and cocoa powder into a small mixing bowl, and set aside.
In a medium mixing bowl, beat the eggs, sugars, salt, and vanilla until thick and pale in color.
Fold the cooled chocolate into the egg mixture, then gently fold in the flour mixture.
Pour the batter into the prepared dish and smooth the top.
Bake for about 25 minutes until the top looks slightly cracked and feels soft to the touch.
Let cool completely on a wire rack before cutting into squares.