Brush the steaks on both sides with oil and season generously with salt and pepper. Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.
In a medium frying pan over medium-low heat on the stove, cook the bacon and onion until the bacon is crisp and the onion is tender, 6 to 8 minutes, stirring occasionally. Remove from the heat.
In a small bowl whisk together the vinegar, mustard, and garlic. Gradually whisk in the oil until emulsified and then whisk in the salt and pepper. Put the mushrooms into a medium bowl, add 1/4 cup 60 milliliters of the vinaigrette, and mix to coat well. Set aside the remaining vinaigrette.
Prepare the grill for direct cooking over high heat (450° to 550°F) and medium heat (350° to 450°F).
Prepare the grill for cooking over high heat (500°F) and medium heat (400°F).
Place a perforated grill pan over medium heat, close the lid, and preheat for 10 minutes.
Spread the mushrooms in a single layer on the grill pan and cook over direct medium heat, with the lid closed, until golden brown and tender, 6 to 8 minutes, turning once or twice. Do not move the mushrooms until the undersides are nice and brown. At the same time, grill the steaks over direct high heat, with the lid closed, until an instant-read thermometer inserted in the center registers 125°F (or your preferred doneness), 8 to 10 minutes for medium rare, turning once or twice. Remove from the grill and let rest for 3 to 5 minutes.
Spread the mushrooms in a single layer on the grill pan and cook over medium heat, with the lid closed, until golden brown and tender, 6 to 8 minutes, turning once or twice. Do not move the mushrooms until the undersides are nice and brown. At the same time, grill the steaks over high heat, with the lid closed, until an instant-read thermometer inserted in the center registers 125°F (or your preferred doneness), 8 to 10 minutes for medium rare, turning once or twice. Remove from the grill and let rest for 3 to 5 minutes.
When the mushrooms are ready, transfer them to the pan with the bacon and onion and warm over medium heat on the stove for about 1 minute, stirring often. Add the chives and mix well. Serve the steaks warm with the mushroom mixture spooned on top. If you like, whisk the remaining vinaigrette to recombine, then drizzle a little over each steak.
