Bring a large pot of salted water to a boil. Add the fettuccine and cook until al dente. Reserve 1/2 cup of the pasta water. Drain the pasta and set aside.
Heat a cast-iron skillet over a medium-high heat. Add the butter, along with the olive oil. Sprinkle the steaks all over with salt and pepper. When the butter has melted and the oil is hot, place the steaks in the skillet and cook for 3 to 4 minutes per side for medium-rare. Remove the steaks to a cutting board to rest.
Add the onion, garlic, tomato paste and red pepper flakes to the skillet, then quickly stir and cook for 1 to 2 minutes. Add the wine and allow to reduce for 30 to 60 seconds, then add the cream. Stir, then add the collards, kale and spinach. Stir and allow the greens to wilt, 2 to 3 minutes. Add the pasta, reserved pasta water and cheese. Toss until everything is coated and the sauce has thickened, about 2 minutes. Remove from the heat.
Slice the steak and shingle the slices over the pasta. Drizzle over the steak sauce and sprinkle over the curly parsley. Serve straight from the skillet.