Toss beef cubes with flour, salt, and pepper in a large bowl until evenly coated.
Heat 2 tbsp oil in a Dutch oven over medium-high heat. Brown beef in batches, adding more oil as needed. Transfer browned beef to a plate.
Add remaining oil to the pot. Sauté onion and garlic for 2–3 minutes until fragrant and translucent.
Stir in tomato paste and cook for 1 minute to develop flavor.
Add carrots, potatoes, parsnips, and celery. Stir to combine with aromatics.
Return beef to the pot. Pour in beef broth and Guinness. Add Worcestershire sauce, bay leaves, thyme, rosemary, and sugar.
Bring to a boil, then reduce heat to low. Cover and simmer for 1.5–2 hours, stirring occasionally, until beef is fork-tender and vegetables are cooked through.
Discard bay leaves. Adjust seasoning with salt and pepper as needed.
Ladle stew into bowls and garnish with chopped parsley. Serve hot with crusty bread.