Flatten the beef round with a cleaver, or meat pounder, to1/4-inch thick, butterfly if necessary. Mix the vegetables together with the garlic. Take half of the diced vegetables and mix with the ground chicken. Season with the salt and pepper, bread crumbs and egg. Mix thoroughly.
Season the beef with salt and pepper. Spread the chicken farce on 1 side of the flattened bottom round and add the pickles lengthwise, directly down the middle of the meat. Carefully roll the beef into a tight roll, being sure not to press too hard or squeeze the chicken farce out of the sides. Season the outside of the beef roulade with salt and pepper. Tie with butcher's string in 5 or 6 sections along the length of the roll. Tie them fairly tight, because when the beef cooks it will shrink and the string will fall off. Sear the beef in a smoking hot saute pan in olive oil until all sides are a dark brown color. Remove from the pan and keep in a warm place.
In the same pan, add the other half of the vegetables and cook for 3 minutes, when the vegetables are golden brown deglaze with wines and add the fresh thyme.
Bring this mixture to a boil, add the beef, and reduce the heat. Cover with either the lid or foil and cook for 20 minutes. Remove the foil and add the veal stock and chicken stock. Bring to a boil and turn the meat, so that the other side of the meat is in the liquid. Cook for 10 more minutes on a medium flame. Cook this mixture until the internal temperature reads 165-degrees F. The chicken must read 165-degrees F or you risk the chance of possible bacteria. If too much of the liquid evaporates, add a little more chicken stock.
Remove the meat from the pan and let rest for 10 minutes prior to slicing. Remove the string from the beef with a small knife. Slice the beef into 1/2-inch portions and transfer to a serving platter. Add butter to the vegetable mixture and swirl to melt. Spoon the vegetable mixture over the meat and serve with chopped parsley.