Preheat oven to 300°F. Line a 9×9-inch pan with foil, leaving an overhang for easy removal, and spray the foil with cooking spray. Set the pan aside.
Put ½ cup unsalted butter (1 stick) in a large microwave-safe bowl. Microwave on high for 1 minute. If the butter is not fully melted, continue heating in 10-second bursts, stirring after each, until melted.
Add 2 cups semi-sweet chocolate chips, a heaping 1/2 cup creamy peanut butter, and 2 tablespoons brewed coffee to the bowl with the melted butter. Microwave on high for 1 minute, then stir. If the chocolate and peanut butter are not fully melted and smooth, heat in 10-second bursts, stirring between each burst, until the mixture is smooth and pourable.
Whisk the melted chocolate mixture until uniform and glossy.
Add 4 large eggs, ⅓ cup granulated sugar, and 1 tablespoon vanilla extract to the chocolate mixture. Whisk until the eggs and sugar are fully incorporated and the batter is smooth.
Add ⅓ cup unsweetened natural cocoa and 1 teaspoon instant espresso granules (optional). Whisk until the cocoa and espresso granules are fully incorporated and the batter is smooth with no lumps.
Pour the batter into the prepared 9×9 pan and smooth the top lightly with a spatula.
Bake about 35 minutes, or until the edges are set and the top and center have just set (not jiggly). A toothpick inserted in the center should come out with a few moist crumbs but no wet batter.
Remove the pan from the oven and place it on a wire rack. Let the brownies cool completely in the pan, at least 2 hours, before adding the drizzles.
When the brownies are completely cool, place ½ cup semi-sweet chocolate chips in a small microwave-safe bowl. Microwave on high about 1 minute, then stir. If not fully melted and smooth, heat in 10-second bursts, stirring between, until smooth and pourable. Drizzle the melted chocolate over the cooled brownies using a spoon or squirt bottle.
Place ⅓ cup creamy peanut butter in a small microwave-safe bowl. Microwave on high about 45 seconds, then stir. If not pourable, heat in 10-second bursts, stirring between, until smooth. Drizzle the warmed peanut butter over the chocolate drizzle.
Cover the pan with foil to prevent fridge odors and chill the brownies in the refrigerator at least 4 hours, or preferably overnight, before serving.