Heat 2 tablespoons of olive oil in a large Dutch oven or heavy pot over medium-high heat. This will be your "cauldron" for brewing the magical stew.
Pat the beef cubes dry with paper towels and season generously with salt and black pepper. Working in batches to avoid overcrowding, brown the meat on all sides, about 3-4 minutes per batch. Transfer the browned meat to a plate and set aside.
Add the remaining tablespoon of olive oil to the pot and reduce heat to medium. Add onions and cook until translucent, about 5 minutes. Add garlic and cook for another 30 seconds until fragrant. Stir in the tomato paste and cook for 2 minutes, allowing it to slightly caramelize for deeper flavor.
Pour in the red wine (or additional broth) and use a wooden spoon to scrape up all the flavorful brown bits from the bottom of the pot. Let the liquid reduce by half, about 5 minutes.
Return the beef to the pot and add beef broth, bay leaves, thyme, and Worcestershire sauce. Bring to a boil, then reduce heat to maintain a gentle simmer. Cover and cook for 1 hour, stirring occasionally.
After the initial hour of cooking, add carrots, parsnips, celery, and potatoes. Return to a simmer, cover, and cook for another hour until the vegetables and beef are tender. If using purple potatoes or cauliflower for a spooky effect, add them during the last 30 minutes to preserve their color.
Five minutes before serving, stir in the frozen peas. They'll cook quickly while maintaining their bright green color, adding a vibrant "potion" element to your cauldron. Remove bay leaves and adjust seasoning with salt and pepper to taste. Garnish with fresh parsley.