Pat the steak dry. Cut into 1 ½ inch pieces. Season with 1 teaspoon of salt.
Heat a large cast iron skillet to high heat, add olive oil. Once hot, add the steak. (Make sure not to crowd the skillet, cook batches if the skillet is smaller.)
Cook for 4-5 minutes, flipping every 1 minutes until all sides are golden brown. Remove to a plate.
Turn the pan to medium-high heat. Add the butter, mushrooms, remaining ½ teaspoon of salt, fresh thyme and saute until tender for about 5 minutes. Add garlic and cook for an additional 1 minute.
Turn the pan to low heat, add mustard, heavy cream and shredded parmesan cheese. Adjust seasoning if needed. Toss to combine.
Add the steak back to the pan and allow to heat through and the sauce to thicken for about 3-4 minutes.
Sprinkle with chopped chives and serve with your favorite sides like pasta, mashed potatoes, cauliflower mash, or rice. Or serve as an appetizer with some toasted baguette.