Set a BBQ on to heat and also heat an oven to 180°C. Combine first four balsamic vinegar, Worcestershire sauce, brown sugar, and garlic in a large ziplock bag. Add the venison steaks and coat well in the bag. Leave to marinate while you prepare the vegetables.
Cut the carrot and parsnips into thin strips like shoestring fries. Place in an ovenproof dish and coat in the vegetable oil. Bake for 20-25 minutes, turning occasionally until well roasted.
BBQ the venison steaks for 2-3 minutes on each side then cover with tin foil and leave to rest for 5 minutes. Blend the parsley, garlic, capers, olive oil, vinegar, and salt until pureed.
To serve, season the vegetable chips and place on 2 warm plates. Cut the rested venison across the grain then place on the plates. Spoon the green sauce over the meat.