Preheat oven to 325F.
Heat the oil in a large, oven safe dutch dutch oven or pot over medium heat. Brown the beef in a single layer for a few minutes each side - complete in batches, do not crowd the pan! Remove to a plate or bowl, meat will not be cooked through.
Add the onions and sauté a few minutes, until translucent. Add the garlic and 2 remaining teaspoons of Italian Seasoning and sauté for another minute, stirring constantly so as to not burn the garlic. Add the tomato paste and balsamic vinegar/wine to deglaze, scraping up any brown bits from the bottom of the pot with a wooden spoon.
Return the browned beef to the pot and the remaining ingredients (except for the frozen peas and fresh parsley). Stir to combine. If the liquid doesn't reach the meat and vegetables, add a bit of water - only as much as is needed to reach the same level as the meat and vegetables (they do not have to be fully submersed). Bring to a simmer.
Cover with a lid, transfer to the oven and braise for 2 hours, or until meat is fall apart tender.
Remove star anise and bay leaf. Taste and adjust seasoning with more salt and pepper if desired. Add the frozen peas, if using, and let sit for a minute or two to cook (they will cook from the residual heat of the stew). Serve garnished with fresh parsley and bread or biscuits for dipping, if desired.