Caramelize the sugar until light brown and stir in two tablespoons of butter. Pour the hot syrup into the bottom of a one and a half liter Gugelhupf tin. Butter the mold well after it has cooled down.
Bring the milk with the sweet cream, the sugar and a scraped half vanilla pod to the boil and let it steep. After cooling, fish out the vanilla pod and mix the eggs and yolks well. If you like, add apricot brandy to taste.
Core the apricots and sixth the halves again. Debark the white bread and cut into a centimeter cube.
Melt the butter in a sufficiently large pan and fry the bread cubes until golden brown on all sides. Pour the egg milk over the cubes, add the apricot pieces, mix briefly and pour into the bundt cake pan. Place in a larger saucepan with boiling water (the water should reach the middle of the pan) and bake in an oven preheated to 180 degrees for an hour. The top can become dark. If you want to avoid this, cover with aluminum foil in good time. Prick a wooden skewer to test it. If nothing sticks after pulling it out, the pudding is ready. Take out of the oven, let it rest for half an hour and only then turn it out. The caramel should have largely liquefied again and cover the surface of the bread pudding.
For the sauce, core the remaining apricots and cut into pieces. Bring to the boil with the sugar, the second half of the vanilla pod and a small glass of water and cook covered for ten minutes until the apricots are very soft. Puree with the hand blender, add a dash of apricot brandy if you like and season to taste again.