Set up a double boiler with a large stainless steel mixing bowl over a pot of simmering water. You can buy a double boiler, but setting one up using the pans you already own is just as easy. Just ensure no water splashes up and gets into the chocolate.
Melt the butter and chocolate in the double boiler, using a spatula to prevent the chocolate from burning while you combine the two ingredients. You want the consistency at the end to be silky.
While the chocolate is melting, whip the sugar, eggs, and egg yolks together in a Kitchen Aid mixer until they triple in volume. For us, it was when the mixture reached the top and was just about to overflow the mixing bowl. You can eyeball what three times the volume would look like if you cut this recipe in half. If you don't have a Kitchen Aid mixer, try using an electric hand mixer. However, without having your hands free, the next steps will be harder. So this is a great recipe to make with your spouse or even your kids. Once the eggs and sugar reach triple volume, slowly fold in the melted chocolate using the spatula to scrape any chocolate sticking to the sides. On the kitchen aid mixer we were using, I ran it at almost full speed while the eggs and sugar were mixing but turned it down to 2 when I folded in the chocolate. With the mixer still running at a slower speed, fold in the sifted flour into the chocolate and egg mixture and immediately stop the machine. Lower and remove the mixing bowl, remove the mixing whisk, and stir the mixture by hand, scraping along the sides to ensure everything is well combined. Be careful not to over-mix at this point. Pour the mixture into the buttered and floured tins and bake at 350° F for about 5 minutes. The sides should be set but the centers should still be quite wiggly.
When done, remove the cakes from the oven and gently remove them from the tins by turning them over and gently tapping the sides and bottom of the tins onto the serving plate.
Sprinkle a little powdered sugar over the top and serve.