Preheat Oven: Preheat your oven to 356ºF (180ºC). Prepare a 9 inch x 12 inch (22cm x 30cm) rectangle baking pan by lining it with parchment paper or greasing and dusting with flour for non-stick pans. Set aside.
Melt Butter: Melt butter first and set aside to cool slightly while you prepare the dry ingredients.
Prepare Coffee: Dissolve the instant coffee in the boiling water and set aside to cool slightly.
Mix Dry Ingredients: In a large mixing bowl, whisk together the flour, cocoa, baking powder, and sugar until well combined.
Combine Wet Ingredients: To the dry mixture, pour in the cooled melted butter, cooled coffee mixture, milk, eggs, and vanilla. Using an electric mixer, beat the mixture on low-medium speed until incorporated, ensuring not to over-mix, just until not flour is visible, about 20-30 seconds. Scrape down the sides.
Transfer Batter: Pour the batter into the lined cake pan, spread it out evenly.
Bake: Bake for 25-30 minutes or until a skewer comes out clean or with a few moist crumbs. Remove from the oven and allow to cool in the pan for 15 minutes before transferring to a wire rack to cool completely.