Boil a large pot of salted water and cook fettuccine according to package instructions until al dente; reserve 1/2 cup pasta water before draining.
Pat steak cubes dry with paper towels and season thoroughly with salt, black pepper, smoked paprika, and red pepper flakes.
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat until shimmering.
Add steak bites in a single layer and sear for 2 minutes per side until a crust forms; remove steak from the pan and set aside.
Reduce skillet heat to medium and add the remaining 3 tablespoons of butter and minced garlic, sautéing for 60 seconds.
Whisk in the heavy cream and simmer for 3 minutes until slightly reduced.
Stir in the Parmesan cheese and nutmeg until the sauce is smooth.
Add the fresh baby spinach to the sauce, stirring until just wilted.
Incorporate the cooked pasta into the skillet, adding reserved pasta water if necessary to reach desired consistency.
Divide pasta into bowls and top with the seared steak bites.