Remove steaks from refrigeration 30 minutes prior to cooking to reach room temperature.
Pat steaks completely dry with paper towels and season aggressively on all sides with salt and black pepper.
Heat oil in a heavy cast-iron skillet over medium-high heat until the oil reaches its smoke point.
Place steaks in the skillet and sear for 3 to 4 minutes per side until a deep crust forms.
Reduce heat to medium; add 2 tablespoons of butter, minced garlic, and the rosemary sprig to the pan.
Tilt the skillet and use a large spoon to continuously baste the steaks with the foaming garlic butter for 1 to 2 minutes.
Remove steaks from the skillet and transfer to a warm plate to rest for 5 to 7 minutes.
Discard excess fat from the skillet but retain the browned bits (fond); return to medium-low heat.
Add remaining 2 tablespoons of butter, heavy cream, and Dijon mustard to the skillet, whisking to deglaze the pan.
Simmer for 2 to 3 minutes until the liquid reduces slightly, then whisk in the Parmesan cheese until smooth.
Adjust sauce seasoning and serve over the sliced rested steaks, garnished with chopped parsley.