Hydrate the cocoa powder. Sift the Dutch-processed cocoa into a small bowl. Pour in the boiling water and stir until smooth. Let it cool while you prepare the other ingredients.

Melt the chocolate. If you use bar chocolate, chop it into small pieces and add them to a heatproof bowl. Microwave method: Heat at 50% power in 30-second intervals, stirring each time until about 75% melted. Then, stir until fully melted. Water bath method: Bring a small pan of water to a simmer, then remove from heat. Place the heatproof bowl directly in the water and let the chocolate melt, stirring occasionally. Avoid water contact to prevent seizing. Set aside to cool until the bowl is no longer hot to the touch.

Whip butter. Add slightly softened butter to the stand mixer. Using the whisk attachment, mix on low to break it up, then whip on high until pale and fluffy.

Add chocolates to butter. Scrape the cooled and melted chocolate into the butter and mix briefly by hand. Whip on high speed for a few minutes, stopping once to scrape down the bowl.

Add the cocoa paste and whip on high for a few more minutes, scraping as needed. Once emulsified, the frosting will appear slightly paler and thicker.

Adjust for taste and smooth out the frosting. Taste the buttercream for sweetness. Add the powdered sugar and salt, mix, and adjust as needed. Once satisfied with the flavor, whip on high for a full minute.

Switch to the paddle attachment and mix on low for at least 3 minutes to smooth out air pockets.

Depending on the chocolate used, the buttercream may seem loose at first. If you like it as is, use it immediately and chill the frosted cakes for 30 minutes to set. For a firmer consistency, briefly chill the bowl in the freezer (about 5 minutes), then mix until smooth.

If the frosting is too stiff, warm it slightly. Melt a couple of tablespoons in the microwave and mix back in, or use a hair dryer on the bowl’s side to gently soften.