In a bowl, combine parsley, olive oil, shallots, red wine vinegar, minced garlic, and red pepper flakes. Add salt and black pepper to taste. Set aside.
In a large bowl, combine ground beef, 1/2 teaspoon salt, 1/2 teaspoon black pepper, and 3 tablespoons of the sauce. Mix well and form into 4 patties, each about 2 cm thick.
Heat 3 teaspoons vegetable oil in a large skillet over medium heat. Add red onion rings and fry, stirring occasionally, for 6 minutes until soft. Transfer to a plate and cover with foil.
Wipe out the skillet with a paper towel. Heat 2 teaspoons vegetable oil over medium heat. Add patties and fry for 4-6 minutes on each side until cooked through (internal temperature 71°C / 160°F).
Place one patty in each hamburger bun. Top with fried onions and drizzle with the remaining sauce.