In a mixing bowl, combine olive oil, lemon juice, minced garlic, red wine vinegar, dried oregano, dried thyme, paprika, salt, and black pepper. Whisk to create the marinade.
Place the beef cubes in a shallow dish or resealable plastic bag. Pour the marinade over the beef, ensuring all the pieces are well coated. Massage the marinade into the beef.
Cover the dish or seal the bag and refrigerate for at least 2 hours, or overnight for optimal flavor infusion.
Preheat the grill to medium-high heat.
Thread the marinated beef cubes onto skewers, leaving space between each piece.
Place the skewers on the preheated grill. Cook for 10-12 minutes, turning occasionally, until the beef is slightly charred on the outside and cooked to your desired doneness.
Remove the beef skewers from the grill and let them rest for a few minutes.
Serve the Souvlaki Beef on a platter, garnished with fresh parsley. Accompany with warm pita bread, sliced tomatoes, sliced red onions, and lemon wedges.