Let the steaks sit at room temperature, to take the chill off, while you heat a grill pan to high. When the pan is very hot, drizzle the steaks with extra-virgin olive oil and season with salt and pepper, to taste. Cook the steaks 3 to 4 minutes on each side for pink centers, a couple minutes longer for medium well. Remove the steaks to a cutting board and let rest about 5 minutes before slicing.
Meanwhile, in a salad bowl combine the garlic, ketchup, mustard, Worcestershire and vinegar. Whisk in 1/3 to 1/2 cup extra-virgin olive oil and season with salt and pepper, to taste. Add the greens and toss. Slice the steaks, arrange on serving plates and top with the salad.