Dab meat dry. Mix 2 tsp. paprika powder, 2 tsp. cayenne pepper, 2 tsp. salt and pepper. Rub the meat with the mixture vigorously, place in a roasting pan. Sprinkle with oil, cover and chill overnight.
The next day, cover the meat in the roaster and braise it in the preheated oven (electric cooker: 125 °C/ circulating air: 100 °C/ gas: see manufacturer) for approx. 6 hours. In between, cover with roasting stock.
For the hamburger buns, stir yeast with 20 g sugar until liquid. Warm the butter and milk. Add 125 ml water and let it cool down lukewarm. Put 1 tsp. salt, flour and egg in a bowl. Add milk mixture.
Add the yeast mixture and immediately knead into an elastic dough with the dough hooks of the hand mixer for 6-8 minutes. Cover and leave to rise in a warm place for about 45 minutes.
For the salad, clean, wash and quarter the cabbage and cut out the stalk. Halve the cabbage quarters again and cut into fine strips. Place in a bowl. Sprinkle with 1/2 tsp salt and knead well.
Peel carrots. Wash the apple, quarter and core it. Cut both into fine sticks. Peel onion and grate roughly. Wash the lamb's lettuce and drain well. Clean the salad and chop finely. Mix cabbage, carrots, apple, onion and salad, season with pepper and 1 tsp. sugar.
Mix crème fraîche, 100 g cream, 4 tablespoons vinegar. Season to taste with salt, pepper and sugar. Mix everything evenly into the cabbage. Let it stand in a cool place.
For the barbecue sauce, peel and finely dice the shallots and garlic. Place in a pot with Worcestershire sauce and maple syrup and bring to the boil. Simmer for 2 minutes. Add ketchup, 2-3 tbsp vinegar, 1 pinch of paprika and 2 tsp cayenne pepper.
Let everything simmer for about 10 minutes, stirring from time to time. Remove meat from the oven. Pluck the meat into small pieces with two forks. Add the meat to the sauce and set aside.
Briefly knead the dough once again on a floured work surface. Form about 8 round rolls from the dough and place them on two baking trays lined with baking paper. Cover them and let them rise for another 20 minutes.
Whisk the egg yolks with 2 tablespoons of cream. Spread the bread roll with it and sprinkle with sesame seeds. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) one after the other for about 15 minutes.
Remove and let it cool down on a cake rack.
Cut the buns in half horizontally. Roast the cut surfaces on the grill or in a hot pan. Warm the meat with the sauce. Season salad again with salt, pepper and sugar. Cover the lower halves of the rolls with plenty of meat and salad.
Put the lid on the roll and serve immediately.