Heat a cast-iron skillet or a large grill pan over high heat. Season the meat with salt and pepper, drizzle with EVOO, and bring to room temperature. To a food processor bowl add the shallot, the grated or finely chopped garlic, the anchovies, parsley, rosemary, sage, red pepper flakes, lots of black pepper, a little salt, and the Worcestershire sauce plus about 1/4 cup EVOO. Pulse to chop the ingredients into a thick green sauce, then transfer to a bowl.
Heat 2 tablespoons of the EVOO in a large nonstick skillet over medium heat with the crushed garlic. Remove the garlic and add the potatoes in an even layer, season with salt and pepper, and cook to brown, 3- 4 minutes on the first side. Turn and cook for 3-4 minutes more, then add the greens to the pan and season with a little nutmeg. Turn off the heat.
While the potatoes cook, throw the steaks into the hot skillet and cook for 7-8 minutes total for pink centers and up to 12 minutes for medium-well, turning once. Serve the steaks with the salsa verde on top and the potato-greens hash on the side.