For the chimichurri: In a bowl, mix together the olive oil, lime juice, parsley, basil, oregano, thyme, garlic and shallots. Season with salt and pepper. Divide the chimichurri between two bowls--use half as the marinade and half as the dipping sauce.
For the steak: Place the steak in a large baking dish and pour over half of the chimichurri. Turn to coat; cover and marinate in the refrigerator for 2 hours.
Preheat a grill to high. Let the steak come to room temperature, then remove it from the marinade and sprinkle with salt and pepper. Grill for 4 to 5 minutes on one side, until browned. Turn, and grill another 4 to 5 minutes for medium-rare. Remove from the grill and let rest for 10 minutes before slicing thinly on the bias.
For the vegetables: Bring a small saute pan with salted water to a boil, and blanch green beans. Remove the beans to an ice bath.
Coat a medium saute pan with olive oil, and bring to high heat. Add the fennel, and sweat about 5 minutes. Add the garlic, and saute until aromatic. Add tomatoes and green beans, and cook until wilted.
Serve the steak and vegetables with the remaining half of the chimichurri sauce on the side.
Recipe courtesy of Anne Burrell