Dissolve the fresh brewer's yeast with half of the lukewarm water. Add the first dough, the flour and the sugar and mix with the dough hook for about 5 minutes, then add the salt and keep kneading adding the water slowly until the dough is smooth and not sticking. You can also do it by hand with a lot of patience. It is a long job, but completely doable.
Add the chopped butter and knead with the dough hook at low speed for about ten minutes, until the mixture has completely absorbed the butter, has become smooth, not too sticky and opaque.
In the last 5 minutes add the chopped chocolate and coarsely diced dried apricots and knead just enough to incorporate them.
Transfer the dough in a greased bowl and let it relax for about 15 minutes in a warm place, as in the closed oven with the little light on.
After this much required rest you can shape the buns, dividing the dough into pieces of 80 g each.
Now you can shape the buns following the links I provided below the recipe. It's not hard, you just need some practice.
Arrange the round buns in two baking sheets lined with parchment paper, allowing them enough space to rise.
Beat an egg with a tablespoon of water and brush gently each bun. Let them rise again for about 25 minutes, then brush again with the egg wash.
Let them rise again until doubled in size.
Preheat oven to 180°C and bake the buns for about 15-20 minutes, until they are golden and well puffed.
Meanwhile, prepare the sugar syrup: boil for about 10 minutes over medium heat the water with the sugar and the open and scraped vanilla bean.
As soon as you take the buns out of the oven, brush them with the hot sugar syrup and let them dry completely.
They are irresistible eaten just out of the oven, when they are still warm and the chocolate is soft, but they will keep well for 5-6 days into a tin box or in a Ziploc bag.