Preheat the oven to 350 degrees F (175 degrees C). Line an 8x8-inch square pan with enough parchment paper to have overhang on all sides.

Stir espresso powder and coffee together in a small bowl until espresso powder is completely dissolved.

Whisk flour, cocoa, cream of tartar, baking soda, salt, and 1/4 teaspoon cinnamon together in a bowl; set aside.

Beat butter, 1/2 cup white sugar, and brown sugar with an electric mixer together until light and fluffy in a bowl. Beat in espresso mixture, egg, and vanilla until well combined.

Stir in flour mixture; mix until a dough just begins to form. Press dough firmly and evenly into the prepared pan using lightly floured hands.

Whisk 1 tablespoon white sugar and remaining 1/2 teaspoon cinnamon together in a small bowl; sprinkle sugar mixture evenly over the dough.

Bake in the preheated oven just until the dough in the center of the pan feels barely set, 20 to 23 minutes.