Remove steaks from refrigeration 30 minutes prior to cooking to reach room temperature.
Pat steaks dry with paper towels and season generously on all sides with salt and pepper.
Heat oil in a heavy cast-iron skillet over high heat until just beginning to smoke.
Carefully place steaks in the skillet and sear for 3-4 minutes per side for medium-rare, or until the internal temperature reaches 130°F (54°C).
Remove steaks from the pan and transfer to a plate; tent loosely with foil to rest for 10 minutes.
Reduce heat to medium and drain excess oil from the skillet, leaving approximately 1 tablespoon of drippings.
Add butter to the skillet and sauté the minced garlic for 1 minute until fragrant but not browned.
Pour in the heavy cream and dried thyme, scraping the bottom of the pan to release any browned bits.
Simmer the cream for 3-5 minutes until slightly thickened, then whisk in the Parmesan cheese until melted and smooth.
Place steaks back into the skillet briefly to coat with sauce then serve immediately garnished with fresh parsley.