Begin the Marsala sauce by heating the olive oil in a large saute pan. Cook the shallots (or onion) and mushrooms gently until they become translucent. Deglaze the pan with the wine and add the stock and fresh thyme. Allow to reduce by two-thirds.
Preheat the grill to medium-high heat and season meat on both sides with salt and pepper. Sear the meat on both sides, and grill to about 128 degrees F internal temperature for medium-rare. Remove meat from grill and let rest.
Strain Marsala sauce and whisk in butter to finish. Season with salt and pepper, as needed. Spoon the sauce over the grilled steaks, garnish with chopped chives, and serve.