Does this type of frosting have a name?

I've previously asked about converting a family recipe for a cocoa frosting to a coffee frosting instead, and got a pretty good answer, but it's all very theoretical and "try this" and "try that", and I just don't have the time or, to tell the truth, the patience, to experiment like that. I think what I want is an established recipe, or rather, a way to search for an established recipe. Problem is, if you search for "coffee frosting", you get various types of buttercreams, all of which involve copious quantities of powdered sugar.

If I could instead search for "coffee [insert type of frosting here]", I might have better luck. Problem is, haven't the faintest idea what this frosting method/technique is called (assuming it has a name).

Here's the recipe:

Ingredients: 2 heaping tableserving spoons Dutch-processed cocoa (the original recipe just calls for 2 big spoonfuls, but in family practice, this has morphed to a whole lot more cocoa than that), 3 to 5 tablespoons granulated sugar (depending on how heavy-handed you were with the cocoa), 5 tablespoons water, 8 egg yolks, 2 sticks unsalted butter.

Method: combine everything except the butter in the top of a double boiler. Cook slowly, stirring pretty much constantly, until very thick and sticky. (It'll take a while, and your arms will get pretty tired.) Let cool. Meanwhile, whip the butter until light and fluffy. Combine the completely cooled chocolate mixture and the butter.

Does anyone recognize this type or method of making frosting? Does it have a name?

Looks like I need to edit to make it clear that it's the method that I'm after, not a vague resemblance of the ingredients.

So, the method, in more detail: combine starch (cocoa powder, in this case), sugar, a relatively large quantity of egg yolks, and a relatively tiny quantity of water. Cook in a double boiler, stirring constantly. If you find yourself scraping thickened mixture off the bottom of the pot while the rest of the mixture isn't as thick, immediately remove from the heat and stir like crazy until smooth. Rinse and repeat, until your arms are screaming, and the mixture is so thick that when you lift the whisk, the cream slowly falls off in clumps, rather than in a solid stream. Let cool completely. When cooled, the mixture is about the same texture as butter, just stickier. Thus, you can simply dump the entire cooked mixture into the butter (or the butter into the mixture, makes no difference), without worrying about curdling or separating, and whip away until no streaks remain.

As you can see, there's no cooking of sugar syrup, there's no hoping-the-sugar-will-cook-the-yolks-without-curdling-them, there's no dropping-the-butter-into-the-cream-in-small-cubes-and-praying-it-incorporates, and there is starch, so it is absolutely, positively NOT a French buttercream. The relatively tiny quantity of liquid means that this doesn't really resemble a German buttercream or a "flour buttercream", either, though a German buttercream made creme mousseline style (i.e. with pastry cream instead of custard) gets tantalizingly close...