Preheat your oven to 400 degrees F.
Rub the steaks with rosemary and garlic, then season both sides generously with salt and pepper.
Heat the olive oil in a large skillet over high heat. When the oil starts to shimmer, add the steaks and sear each side for about 2 minutes. Transfer the steaks to a baking sheet and roast in the oven until the internal temperature reaches 120 to 125 degrees F for medium-rare to rare, about 8-12 minutes. Remove from the oven, cover tightly with foil, and let rest for 10 minutes.
While the steaks are resting, prepare the sauce. Melt the butter in a skillet over medium-high heat. Add the shallots and mushrooms, seasoning with salt and pepper. Cook undisturbed for 5 minutes, until golden, then stir and continue cooking for another 3-5 minutes until the mushrooms are caramelized. Remove the mushrooms from the skillet and set aside on a plate.
Pour the vegetable broth into the skillet, scraping up any browned bits from the bottom. Simmer for 3-5 minutes until the broth has reduced by about a third. Slowly add the cream and dijon mustard, bringing the sauce to a boil. Reduce heat to low and simmer for 5 minutes until the sauce thickens slightly. Remove from heat and stir in the parmesan. Season with salt, pepper, and crushed red pepper flakes. Return the mushrooms to the sauce and stir to combine.
Serve the steaks topped with flaky salt and spoon the sauce over them. Enjoy!