Brush the steaks with 1 tablespoon of butter. Preheat a large nonstick skillet over medium-high heat.
Add the steaks and cook, without turning, until moisture appears (3 to 4 minutes). Turn and cook for 3 to 4 minutes more, for medium.
Transfer the steaks to a plate, cover with foil, and let rest for 5 minutes. Meanwhile, in the same skillet, melt the remaining 1 tablespoon butter. Add the mushrooms and cook until softened. Add the cream and simmer until reduced and thickened. Season with sea salt and pepper to taste.
Pour the mushroom sauce over the steaks and serve.