Preheat a grill to high. Whisk the mustard, olive oil and Worcestershire sauce in a small bowl. Season the steak with salt and pepper, then coat with half of the mustard mixture; let sit at room temperature 10 minutes. Combine the sour cream and chives in another small bowl and season with salt and pepper; refrigerate until ready to use.
Transfer the steak to the grill and cook 5 minutes; flip, brush with half of the remaining mustard mixture and cook 5 more minutes. Flip again and brush with the rest of the mustard mixture; cook 5 to 8 more minutes for medium rare. Transfer to a cutting board and let rest.
Meanwhile, bring a large pot of water to a boil. Add the pierogi and cook as the label directs. Put the spinach in a colander. Drain the pierogi in the colander with the spinach so the spinach wilts. Return the pierogi and spinach to the pot and stir in the butter; season with salt and pepper.
Slice the steak against the grain; divide among plates along with the pierogi and spinach. Top the pierogi with the chive sour cream.