Heat the oven to 350° F (177° C). Grease an 8-inch or 9-inch square metal cake pan with butter or cooking spray. Line the pan with one long sheet of parchment cut to cover the bottom and two sides. Smooth the parchment with your hands, creasing it into the corners for a snug fit.

In a medium saucepan, combine the cocoa powder and instant coffee. Add the milk, a splash at a time, while whisking constantly, until the cocoa is evenly dissolved. Add the butter cubes and cook over medium heat, stirring and scraping frequently with a stiff silicone spatula, until the butter is melted and the mixture comes to a simmer, about 5 minutes. Cover and remove from the heat.

In a stand mixer fitted with the paddle (or in a larger bowl with a hand mixer), combine the powdered sugar, rice flour, and salt and mix on low until evenly combined, about 1 minute. Add the eggs and vanilla and mix on low speed until moistened, then increase the speed to medium and mix until smooth and creamy, about 1 minute. Stop to scrape the paddle and the bowl.

With the mixer running on low, stream in the hot milk mixture. Stop to scrape the paddle and the bowl, then increase the speed to medium and mix for at least 2 minutes.

Pour the mixture into the prepared pan and bake until the brownie bounces back when you press the center, 40 to 50 minutes. Cool for at least 10 minutes in the pan, then use the parchment to lift the brownies out of the pan. Use a sharp knife to cut into 16 portions. Dust with cocoa if you like.