In a large, heavy-bottomed pot or Dutch oven, heat the olive oil over medium-high heat. Add the beef stew meat and brown it on all sides. Work in batches if necessary to avoid overcrowding the pot. Once browned, remove the meat and set it aside.
In the same pot, add the diced onion and sauté until softened and translucent. Add the minced garlic and cook for an additional minute, being careful not to burn it.
Pour in the beef broth and red wine (if using), stirring to deglaze the pot and scrape up any browned bits from the bottom. This adds incredible flavor to the stew.
Stir in the tomato paste, bay leaves, dried thyme, dried rosemary, paprika, salt, and pepper. Return the browned beef to the pot, and bring the mixture to a boil. Once boiling, reduce the heat to low, cover, and let the stew simmer for about 1.5 to 2 hours or until the beef becomes tender and starts to fall apart.
Add the carrot and potato chunks to the stew, and continue to simmer for an additional 30 minutes or until the vegetables are cooked to your desired tenderness.
If using frozen peas, add them to the stew during the last 5 minutes of cooking to preserve their vibrant color and freshness.
Taste the stew and adjust the seasoning as needed. Remove the bay leaves before serving.
Ladle the hot and aromatic Beef Stew with Carrots and Potatoes into bowls, garnish with fresh chopped parsley, and serve with crusty bread or fluffy rice for a hearty and satisfying meal.