Cook bacon in heavy large pot over medium heat until crisp, about 5 minutes. Using slotted spoon, transfer bacon to paper towels to drain. Reserve bacon drippings in pot.
Sprinkle beef with salt and pepper. Place flour in large bowl. Toss meat in flour, shaking off excess and reserving remaining flour in bowl. Heat drippings in pot over medium-high heat. Working in 2 batches, add beef to pot and cook until just browned, stirring frequently, about 5 minutes per batch. Transfer meat to large bowl.
Add onion and garlic to pot and sauté until tender, about 5 minutes. Add remaining flour and stir 1 minute. Mix in broth, beer, tomato paste, 2 tablespoons thyme, and sugar. Reduce heat to medium; simmer until mixture thickens slightly, scraping up browned bits, about 15 minutes. Add beef, 1 tablespoon thyme, and 3 tablespoons parsley. Simmer until beef is cooked as desired, about 5 minutes for medium-rare. Season with salt and pepper. Transfer stew to bowls, sprinkle with 1 tablespoon parsley and reserved bacon bits, and serve.
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