Once the dough is steaming and fragrant, immediately remove pan from heat and transfer the dough to the bowl of a freestanding electric mixer fitted with a paddle attachment. Beat on medium speed for about 1 minute to release some of the heat from the cooked dough, before turning down the mixer to its slowest speed and adding 4 eggs, one at a time, only adding the next egg until the previous one is fully incorporated. Stop the mixer between each egg addition to scrape down the bowl. After the last egg, the mixture should be glossy and thick — when scooped with a spoon, the dough should slowly pour off the spoon.