Heat a large heavy-bottomed skillet over medium-high heat. Sprinkle steak with 1 teaspoon of the salt and 1/2 teaspoon of the pepper; place in skillet and cook 8 minutes, turning half-way through, for medium-rare. Remove from skillet and keep warm.
Add oil to skillet and cook mushrooms 3 minutes; remove from skillet and keep warm.
Raise heat to high; add broth, wine, and garlic and cook until reduced to 1/2 cup, 10 minutes. Stir in remaining salt and pepper.
Remove 4 tablespoons of broth mixture and toss with spinach in a large bowl; divide spinach among four plates.
Top with sliced steak and mushrooms; drizzle with remaining broth mixture.