Whisk together the Worcestershire sauce, mustard, thyme and salt and pepper, to taste, in a medium bowl until combined. Slowly whisk in the olive oil until emulsified. Let sit at room temperature while you prepare the steak and onions.
Remove the steaks from the refrigerator 20 minutes before grilling. Heat the grill pan over high heat until it begins to smoke. Pat the steaks dry with paper towels. Brush both sides of the steaks with canola oil and season well with salt and pepper. Arrange the steaks on the grill pan and let cook until golden brown and charred, about 5 minutes. Flip the steaks, lower the heat to medium and continue cooking to medium-rare doneness (130 degrees F internal temperature on an instant-read thermometer), about 4 minutes longer. Remove from the heat and arrange on a serving platter. Loosely tent with foil and let rest while you grill the onions.
Brush the onions on both sides with canola oil and season with salt and pepper, to taste. Grill until golden brown and slightly charred on both sides and just cooked through, about 2 minutes per side. Separate the slices into rings and add to a small bowl. Add half of the vinaigrette to the onions and gently toss to coat. Serve the steaks topped with the onions and drizzled with the remaining vinaigrette.