Adjust an oven rack to the lower middle position and heat oven to 325 degrees. Pat beef dry with paper towels and sprinkle with salt and pepper. Heat 1 tablespoon oil in large skillet over medium-high heat until just smoking. Cook half of beef until browned on all sides, about 8 minutes. Transfer to a bowl and repeat with 1 more tablespoon oil and remaining beef. Transfer the beef to the bowl.
Add remaining tablespoon of oil, onions, and 1/4 teaspoon salt to skillet
and cook until onions are lightly browned, about 5 minutes. Add tomato paste and garlic and cook until fragrant, about 30 seconds. Stir in flour and cook for 1 minute.
Stir in broth and 1 1/4 cups of the beer, scraping up any browned bits. Stir in thyme, bay leaves, brown sugar, and browned beef with any accumulated juices. Bring to a simmer, cover, and transfer to oven for 1 hour.
Stir in potatoes and carrots and cook in oven, covered, until beef and vegetables are tender, about 1 hour. Discard bay leaves, stir in remaining 1/4 cup beer, and season with salt and pepper to taste. Stir in parsley before serving.