Prepare a medium fire in the grill. Rub the steaks all over with the olive oil and 1 tablespoon of the soy sauce. Season them generously with pepper.
In a medium bowl mix the remaining tablespoon of soy sauce, the mustard, tomato paste, yogurt, wine and rosemary. Season with salt and pepper to taste and set aside.
Melt the butter in a large skillet set over medium heat and sauté the mushrooms, stirring occasionally, until just browned and tender, about 5 minutes.
Grill the steaks, letting each side get a bit crusty for a total of 8 to 10 minutes for rare to medium rare. Transfer the steaks to a warm platter and tent them with foil while they rest for about 10 minutes.
Set the skillet with the mushrooms over low heat and add the reserved sauce along with any accumulated juices from the platter the steak is on. Simmer, stirring occasionally for 1 to 2 minutes. Spoon the sauce over the steaks and serve immediately.