In a bowl, combine meat with Worcestershire, salt, pepper and herbs. Divide the mixture into 4 portions then form each portion into patties, making them thinner at the center for even cooking. Drizzle burgers with 1 tablespoon EVOO.
Heat a cast-iron skillet over medium-high heat. Cook burgers 10 minutes for medium-rare and up to 16 minutes for medium-well, turning them once halfway through.
Meanwhile, in a saucepan heat 1 tablespoon EVOO and 2 tablespoons butter over medium heat. Add mushrooms and cook 7-8 minutes. Add onions and garlic, and cook 7-8 minutes more, until tender. Season with salt and pepper, stir in flour, cook 1 minute then stir in wine and stock. Bring to a bubble, reduce heat and let thicken. Stir in sour cream and turn off heat.