Preheat the oven to 350 degrees F. Spray an 8x8-inch pan with nonstick spray. Line with parchment paper and let it hang over two sides. Spray the parchment too.
In a medium bowl, sift together the flour, cocoa powder, and salt; set aside.
In a large saucepan, combine the butter and espresso powder. Heat on low and stir until the butter has melted. Add the chocolate, and stir constantly until the mixture is smooth. Remove from heat and stir in both sugars until combined. Let cool slightly.
Whisk the eggs and vanilla into the chocolate mixture and keep moving the batter around until combined and no longer grainy-looking. Add the flour mixture to the batter and stir just until combined. Stir in 1/2 cup of the chocolate chips.
Pour the batter into the prepared pan; smooth the top with a greased spatula. The batter will be very gooey. Sprinkle the remaining 1/4 cup of chocolate chips on top. Bake until a toothpick inserted in the center comes out with a just a few moist crumbs attached (28 to 30 minutes). Don't over bake! Let cool completely before cutting.