Prepare the stuffing: Peel and halve 2 hard-boiled eggs. Cut 1 piece soft sausage into thin strips. Cut 2 small dill pickles in half or quarters lengthwise, depending on how big they are. If the ingredients are too large, simply trim them when filling the beef slices.
Prepare 4 slices beef round: Use a meat mallet to gently tenderize the beef on both sides. The final result should be a slice of meat that is twice as long as it is wide and no thicker than ¼ inch.
Season with salt and ground black pepper on both sides. Slather one side with a layer of mustard. On the top half of each piece of beef, place half of a boiled egg, a piece of bacon, a slice of soft sausage, an onion wedge, and some pickles.
Roll the meat slowly from top to bottom, tucking in the sides as you go. Finally, tie it securely with kitchen twine. Don't hesitate to tighten the string a bit; the meat will shrink during cooking, and you don't want the contents of the roll to fall out.
Sear the meat: Heat 2 Tablespoons sunflower oil in a saucepan over medium-high heat and brown the beef rolls on all sides.
Make a gravy: Transfer the browned roll-ups to a plate and set aside. Add the rest of onion and bacon to the pan with the browned bits. Reduce the heat to medium and cook the onions, stirring often, until they are golden, about 5 minutes. If necessary, add 1 Tablespoon of water. Sprinkle in 1 ½ Tablespoons all-purpose flour and stir for an additional 1 minute.
Add the remaining mustard and stir. Pour in ⅓ cup pickle brine and 4 cups beef broth, then stir to combine. Return the meat to the pan, bring to a boil, reduce the heat to low, cover with a lid, and simmer gently for 1½ hours or until the meat is fork-tender.
Take the finished roll-ups out, remove the string, and set the meat aside on a plate. Season the gravy with salt and pepper, then blend it briefly with an immersion blender until smooth. Return the beef rolls to the sauce and let them warm through.