Preheat the oven to 425°F. Prepare the round steak by removing any fat and tendons on it, then cut the whole steak in half lengthwise. The steak should have doubled in length so that it ends up being about 3½ feet long. Make 2 long cuts up almost the entire length of the beef, stopping before you cut all the way through to create 3 separate strands, each about 2 inches wide. Braid the strands of beef together until the entire round steak is braided, then secure the loose ends with a wooden skewer.
Place a large oven-safe bowl on a baking tray, wrap the braided beef around it, and secure the braid in place with a wooden skewer. For the garlic & herb butter, stir together the softened butter, garlic, thyme, rosemary, salt & pepper. Distribute the garlic & herb butter around the braided beef, tuck sprigs of rosemary into the braid, and season the beef with salt & pepper. Transfer the baking tray to the oven and bake the braided beef bowl at 425°F for 13 minutes. Reduce the temperature in the oven to 325°F and let the braided beef bowl cook for another 10–15 minutes. Once it's done baking, remove the braided beef bowl from the oven and let it rest at room temperature for at least 15 minutes. Collect the drippings from the beef and set them aside for later.
Boil the potatoes in water until they become tender. Drain the potatoes and mash them together with the butter, warm milk, and salt until they become smooth and creamy.
Fry the diced red onions, sliced mushrooms, diced carrots, and diced celery in olive oil. Add in the balsamic vinegar, sprigs of thyme & rosemary, tomato paste, and mustard. Gradually pour the vegetable broth into the frying pan and let everything simmer until the gravy thickens slightly.
Place a piece of parchment paper on a clean cutting board and position the braided beef bowl on top. Spoon the mashed potatoes into the braided beef bowl and create a large well in the center. Pour the vegetable gravy into the well in the center of the mashed potatoes. Season everything with salt & pepper and garnish the mashed potatoes with chopped parsley. If the beef looks too dry, brush it with the beef drippings you collected earlier.
