Heat oil in a large nonstick skillet over medium heat, until hot.
Add mushrooms and 1 teaspoon garlic; cook and stir for 2–4 minutes, or until mushrooms are tender and browned.
Remove to a medium bowl; cool slightly.
Separately, combine remaining 2 teaspoons garlic and thyme.
Press evenly onto beef steaks.
Place steaks in same skillet over medium heat; cook 10–13 minutes, (130–135 degrees for medium rare and 140–145 degrees for medium doneness), turning occasionally; remove to platter.
Add tomatoes, salad greens, and vinaigrette to mushrooms; toss lightly to coat.