Remove the ribeye from the refrigerator 30 minutes before cooking. Pat it completely dry with paper towels, then coat both sides and edges with a mixture of kosher salt, black pepper, garlic powder, and smoked paprika.
Mince 4 garlic cloves for the Alfredo sauce and smash 2 additional cloves for basting; freshly grate the Parmesan, chop the parsley, and measure out all remaining ingredients before you begin cooking.
Fill a large pot with 4 to 6 quarts of water and bring to a rolling boil over high heat; season generously with kosher salt until the water tastes pleasantly salty. Do not add pasta yet.
Heat a cast iron skillet over high heat for 2 to 3 minutes until smoking, add olive oil, then sear the steak undisturbed for 3 to 4 minutes per side. In the last 2 minutes, add butter, smashed garlic, and thyme sprigs, then baste continuously until the steak reaches your desired internal temperature.
Transfer the steak to a cutting board, tent loosely with foil, and rest for 8 to 10 minutes to allow the juices to redistribute before slicing.
Cook fettuccine in the boiling salted water until 1 minute shy of al dente according to package directions; scoop out 1/2 cup of pasta water before draining and set it aside.
In the same skillet over medium-low heat, melt 3 tablespoons of butter, cook the minced garlic for 1 to 2 minutes, then pour in the heavy cream and simmer for 3 to 4 minutes; add the Parmigiano Reggiano in three batches over low heat, stirring constantly, then season with salt, pepper, and nutmeg. Adjust consistency with reserved pasta water as needed.
Add the drained fettuccine to the Alfredo sauce and toss with tongs over low heat for 1 to 2 minutes until every strand is well coated; add a splash of pasta water if the sauce tightens too much.
Slice the rested ribeye against the grain into thin strips, about 1/4 to 1/2 inch thick.
Divide the Alfredo pasta into serving bowls, arrange steak slices on top, and garnish with freshly chopped parsley, extra grated Parmesan, and red pepper flakes if desired; serve immediately.