Pre-heat the oven to 375°F. Heat an outdoor grill or cast iron skillet over medium-high.
Arrange the bacon on a broiler pan or parchment-lined baking sheet. Bake until crisp, 15-18 minutes, then chop.
Season the steak with the Worcestershire and salt and pepper; drizzle with EVOO. Cook to desired doneness, 4-5 minutes per side for medium-rare. Let rest for 5 minutes.
In a large bowl, whisk the lemon juice, garlic, mustard and vinegar. While whisking, slowly stream in 3 tablespoons EVOO; season. Toss the greens and onions with the dressing; divide among plates.
Slice the steak against the grain. Top greens with the steak, bacon and cheese.