Preheat oven to 325°F, with the rack in the bottom position.
Pat the beef pieces dry, and season them well with salt and pepper. Heat a large Dutch oven over medium-high heat. Add 1 tbsp of oil, and place beef pieces in, ensuring not to overcrowd. In batches, brown the pieces on each side and then remove and place onto a plate. Continue browning in batches until all the beef has been browned (typically this takes me 3-4 batches). Set aside the plate of browned beef.
Turn the heat down to medium and add the onions to the Dutch oven. Fry until the onions begin to look translucent, about 3 minutes. Add the garlic and thyme, cook for an additional minute. Then add in the balsamic vinegar and the tomato paste, cook for 2 minutes. Then add the browned beef and it’s juices back into the Dutch oven. Sprinkle with the flour, and stir until well combined and the flour dissolves.
Add in the wine, beef broth, bay leaf, sugar, salt, pepper and parmesan rind. Stir to combine. Cover the Dutch oven with the lid and place into the oven. Braise for 2 hours.
After 2 hours, remove the Dutch oven from the oven, and add in the carrots and baby potatoes. Return to the oven to braise for 55 more minutes.
After 55 minutes, add the frozen peas, and cook for an additional 5 minutes. Remove from oven, remove the bay leaf and parmesan rind, and serve.
(Optional) If reheating, place into the oven at 350°F until hot.