Cook pappardelle in water with the tablespoon salt until 1 minute short of the package time. Reserve 1 cup pasta water before draining.
Meanwhile, pat steak dry and season with its salt and pepper. Heat oil in a large skillet over medium-high heat and sear for 4 to 6 minutes per side until the center reaches at least 145°F; transfer to a board and rest for at least 3 minutes.
Reduce heat to low and remove any blackened loose bits from the skillet. Melt butter, add cream and milk and simmer gently for 2 minutes, scraping up the browned meat juices.
Add pasta and 1/4 cup reserved water and toss for 1 to 2 minutes until tender. Remove from heat and melt Parmesan into the sauce, using more water if needed.
Slice rested steak thinly across the grain and serve over the pappardelle, spooning a little sauce beside the beef.