Pat steaks dry with paper towels and season generously with salt and pepper. A dry surface ensures a perfect crust.
Heat the skillet over medium-high and add half the butter plus olive oil. When hot, place steaks in the pan with smashed garlic and thyme. Sear 3–5 minutes on one side, then flip and baste with remaining butter for another 2–4 minutes to your preferred doneness.
Transfer steaks to a plate and tent with foil. Keep the skillet hot and add mushrooms; sauté 3–5 minutes until tender. If the pan seems dry, add a little oil.
Wipe the pan lightly, pour in balsamic vinegar and honey, then simmer over medium-high. Reduce heat to medium-low and cook 5–8 minutes until the glaze thickens and turns syrupy.
Return steaks and mushrooms to the pan, spoon the glaze over them, and let everything soak for a minute or two. Garnish with fresh thyme and serve immediately.