Preheat oven to broil.

In a large sauté pan over medium-high heat, heat 2 tablespoons EVOO and 2 tablespoons butter. When the butter is melted, add the sliced onions, bay leaf, thyme, salt and freshly ground black pepper and cook until caramelized, about 15 minutes, or until melted down, brown and sweet.

While the onions are cooking, place steak on a broiler pan and generously coat it with EVOO, salt, and freshly ground black pepper. Broil under the broiler for 10 minutes or until cooked to desired doneness. When done, remove and let the steak rest to let the juices return to the center of the meat, about 5 minutes.

In a medium-size pot over high heat, boil water. Once at a boil, add the green beans and cook for 5 minutes, until cooked through.

In a medium-size skillet melt 1 tablespoon butter, add cooked green beans to the pan, juice from half a lemon, salt and freshly ground black pepper. Toss to coat and heat through.

In a medium-size skillet over medium-high heat, melt remaining 2 tablespoons of butter. Add flour to the melted butter and cook about 1 minute. Whisk in chicken stock and milk and season with salt and freshly ground black pepper. Let it come up to a bubble and thicken then turn off the heat. Add the cheese and stir in a figure-eight motion until mixed.