For the mayonnaise, wash the lime hot, grate dry and finely grate the peel. In a narrow tall beaker, whisk the egg yolk, 2 tbsp lime juice, lime zest, mustard, 1/4 tsp salt and 100 ml oil with a hand blender until creamy.
Season to taste with cayenne pepper, paprika and salt. Cover and put in a cool place.
Onions peel, halve and in fine strips cut. Wash the rosemary, shake dry, remove the needles and chop finely. Heat 4 tablespoons of oil in a frying pan. Caramelize onions with sugar while turning for 3-4 minutes.
Finally add rosemary. Season with salt. Remove the onions from the pan and let them cool down.
Clean the salad, wash and spin dry. Wash, clean, grate dry and slice the tomatoes. Cut rolls in half horizontally and roast them one after the other in a hot pan for about 2 minutes with the cut surfaces facing down.
Drain the bacon in a large frying pan brushed with oil until crispy. Drain on kitchen paper. Cut cheese into 4 slices. Place one slice of cheese on each slice of ham. Fold the ham over the cheese.
Rinse meat cold, dab dry and season with salt. Heat 2 tablespoons of oil in a large frying pan. Brown the meat in it for about 2 minutes, turn it, season with steak pepper and place ham packets on top.
Continue frying for about 2 minutes. Take it out.
Spread the undersides of the rolls with mayonnaise. Cover lettuce, tomatoes, meat with ham packets, bacon and onions. Spread the cut surfaces of the upper roll halves with chimichurri and place on top.