In a medium bowl, whisk together olive oil, soy sauce, balsamic vinegar, Worcestershire sauce, minced garlic, Dijon mustard, rosemary, thyme, brown sugar, smoked paprika, and red pepper flakes until fully combined.
Place steaks in a large resealable plastic bag or shallow dish. Pour 3/4 of the marinade over the steaks, reserving 1/4 for later. Seal or cover, ensuring steaks are fully coated. Refrigerate for at least 30 minutes or up to 4 hours.
Preheat grill to high heat (450-500°F). Clean grates thoroughly and oil them lightly with a high-smoke-point oil (like canola) using tongs and a folded paper towel.
Remove steaks from marinade, letting excess drip off. Discard used marinade. Pat steaks dry with paper towels, then season both sides generously with salt and pepper. Place steaks on the hot grill. Cook for 4-5 minutes per side for medium-rare (135°F internal), or adjust time for desired doneness.
While steaks grill, pour the reserved marinade into a small saucepan. Bring to a simmer over medium heat and cook for 3-4 minutes, stirring occasionally, until slightly thickened. Remove from heat.
Transfer grilled steaks to a wooden board or plate. Let rest for 5-7 minutes to allow juices to redistribute. Brush lightly with the warm glaze.
Arrange steaks on a wooden board. Drizzle with any remaining glaze, sprinkle with chopped parsley, and serve with lemon wedges on the side.