Add all the ingredients for the dough to a bowl, mix well, knead into a supple dough, and refrigerate for about 1 hour.
Preheat the oven to 350°F. Take the dough out of the fridge, halve it, and roll both halves out to the same size and roundness. Put one half on a baking tray lined with parchment paper and place the brie wheel in the middle.
Carefully cut the lid off the brie, sprinkle rosemary, chives, and garlic on top of the cheese, and put the brie lid back on.
Spread the sauerkraut evenly around the cheese on the dough.
Place the other dough circle on top and press both halves together well.
Spread a thin layer of mustard around the hidden cheese wheel.
Use a knife to make 16 evenly-spaced incisions around the dough circle, going from the edge of the dough to the cheese in the middle.
Fry the sausage links until golden brown, let them cool down a bit, and then place 1 link on each dough slice.
Roll the dough around each sausage link.
Brush the egg wash over the dough, sprinkle sesame seeds on top, and bake for about 60 minutes.
Once it's cooled a little, your sausage sun is ready to be served. All you have to do is take the lid off the cheese and dunk the pigs in a blanket in all that creamy goodness.