Preheat broiler. Take the steak out of the refrigerator and let it come up to room temperature.
In the meantime, heat the EVOO, about 2 turns of the pan, and 2 tablespoons of butter in medium saucepot over medium-high heat. Once the butter is melted, add the mushrooms and cook about 5 minutes, until brown.
Add the onion, garlic, carrots, parsnips and herbs. Cook until veggies are tender, about 4-5 minutes. Add the potatoes and 3 cups of stock plus one cup of water. Bring up to a bubble then reduce heat and simmer 20-30 minutes.
As the liquid simmers, place the London broil on a broiler pan. Rub it with about 2 tablespoons of EVOO and season it generously with salt and freshly ground black pepper.