Place the eggs, egg yolks, and milk in the bowl of an electric mixer first, then the flours, yeast, sugar, malt, and salt, and finally the butter on top. Mix on low speed with the dough hook attachment until all of the ingredients have been thoroughly combined and the sides of the mixing bowl are clean. Mix on high speed until the dough has reached full gluten development. The final dough temperature should be 27°C / 80°F.
Bulk ferment the dough for 20 to 30 minutes. Portion into 20-g/.71-oz pieces and shape into rounds. Refrigerate covered with plastic (or freeze if making ahead). Do not refrigerate for more than 36 hours, since the yeast will over-ferment.