Just melt the butter over low heat and then let it cool down. When the yeast milk has thick bubbles and has doubled its volume, add the egg, melted butter and the broth and knead everything for 5 minutes with the dough hook. The dough should turn smoothly away from the bowl wall at the end. Lightly oil a fresh bowl, shape the dough into a round shape, put it in, close the bowl and put it back in the warm oven (see above) for 60 minutes.
After the dough has rested, it should have at least tripled its volume. Then knead the strongly risen dough on the unfloured (!) Work surface 1 x briefly to force the air out. For the rolls, divide it into 8 equal portions and grind each one round. That means, first roll the portions into a ball, flatten it lightly and then press the edge downwards with your thumb and forefinger of one hand, so that the dough bulges out like a smooth ball in the middle and a rosette-like opening is created below. Press this opening together a little and then use it to place the blank on the baking sheet lined with baking paper or foil. The distance between the individual blanks should be quite large, as they will still rise considerably after the dough has rested again and also during baking.
For burger buns, divide the dough into just 4 portions, otherwise the rest of the procedure is the same as for the buns.
When all are finished, cover the tray with a cloth and place it in the still warmed-up oven for 30-40 minutes. With this renewed dough rest, the blanks should have increased in size by half. This happens again when baking.
When the dough rest is over, preheat the oven to 160 ° convection. Then mix the egg yolks with the milk and brush the buns with it twice. Sprinkle the larger burger buns with a little light sesame seeds as desired. Slide the tray into the oven on the 2nd rail from below. The baking time is 15 minutes. If the fan is circulating halfway through the baking time, turn the tray once if the buns only brown on one side (unfortunately this is the case with my oven).