Trim excess exterior fat and pat steaks very dry. Season generously with salt and pepper.
Position racks in the upper-middle and lower-middle slots and preheat oven to 375°F. Place a wire rack inside a disposable roasting pan and spread 2 cups salt in the bottom to catch drippings.
Place steaks on the rack and bake on the lower-middle rack. For 1-inch steaks about 6 minutes for 2-inch steaks up to 10 minutes.
Pull from oven. Flip, pat dry, and rest 10 minutes. Meanwhile, preheat broiler to high. Move pan to the upper rack and broil, flipping every 2–4 minutes, until internal temp reaches 125–130°F (medium-rare).
Rest steaks 5 minutes, then slice thinly against the grain. Reserve juices.
Boil pappardelle in well-salted water until al dente. Reserve 1 cup pasta water, then drain.
Heat olive oil and 1 tablespoon butter in a wide skillet. Add mushrooms, season lightly, and cook undisturbed until browned, 6–8 minutes. Add garlic for 30 seconds, then remove mushrooms.
Melt remaining 2 tablespoon butter in the same skillet. Whisk in flour and cook 1–2 minutes. Slowly whisk in milk and simmer until lightly thickened. Stir in Parmesan, pepper, and nutmeg or thyme.
Return mushrooms to the sauce, add pasta, and toss with pasta water as needed. Fold in steak slices and reserved juices. Serve immediately.
