Combine the ground beef, parsley, scallion, salt and pepper. Divide evenly into 4 portions and shape each into 3/4"-1" thick oval patties, about the size and thickness of hamburgers. Place flour in a shallow dish and dredge each patty. Reserve any remaining flour.
Heat the olive oil and the tablespoon of butter in a deep sided skillet or sauté pan over medium-high heat. Add patties and sauté 3 minutes on each side until browned. Do not cook all of the way through. Remove from pan to a plate and cover with aluminum to keep warm.
Add onions and sugar to the pan and sauté 5 minutes, scraping up the fond or brown bits in the bottom of the pan. Stir in garlic and cook 1 minute. Make a well in the center of the pan amidst the onions. Add the tomato paste to the well and sauté until paste begins to brown. **Be sure to allow the tomato paste to brown and even to burn slightly. Keep moving the paste around the well using a metal spatula to keep it from burning completely.
Sprinkle onions with reserved flour and cook 1 minute. Stir in the wine and scrape the fond. Then add the salt and Herbs de Provence or thyme. Stir and scrape the fond again. Add the beef stock all at once. Again stir and scrape the fond. Reduce heat to a simmer.
Return the steaks and their juices to the pan. Cover and simmer for 15 to 20 minutes. I like to simmer for 15, then off heat, uncovered for another 5 to 10 to allow the sauce to thicken upon standing.