Preheat the broiler. Bring a large pot of water to a boil. Meanwhile, put the steak on a foil-lined baking sheet. Rub both sides with the Worcestershire sauce and 1 teaspoon olive oil; season generously with salt and pepper. Broil, turning once, until a thermometer inserted into the center registers 125˚ F to 130˚ F for medium rare, 4 to 6 minutes per side, depending on the thickness. Transfer to a cutting board to rest, about 10 minutes.
Meanwhile, combine the kale, basil, garlic, lemon zest, a pinch each of salt and pepper and the remaining 3 tablespoons plus 2 teaspoons olive oil in a food processor. Mix, scraping down the food processor occasionally, until mostly smooth, adding 1 to 2 teaspoons water to thin the pesto as needed. Transfer the pesto to a large bowl and stir in 3 tablespoons Parmesan and the lemon juice; season with salt and pepper.
Season the boiling water generously with salt. Add the pierogi and cook as the label directs, adding the peas during the last 2 minutes of cooking. Reserve 1/2 cup cooking water, then drain. Add the peas and pierogi to the pesto and stir well to combine, adding a few splashes of cooking water as needed to coat the pierogi evenly; season with salt and pepper.
Thinly slice the steak against the grain and season with salt. Divide the steak and pierogi among plates. Sprinkle with the remaining 1 tablespoon Parmesan and torn basil.