In a large pot or Dutch oven, heat olive oil over medium-high heat. Add beef in batches, searing until browned on all sides. Remove and set aside.
In the same pot, add butter, diced onion, garlic, carrots, and celery. Sauté for 5–7 minutes, until veggies are softened.
Sprinkle flour over the vegetables and stir to coat. Cook for 1–2 minutes to remove the raw flour taste.
Slowly pour in the beef broth while stirring. Add the browned beef back to the pot, along with potatoes, thyme, rosemary, salt, and pepper. Bring to a boil, then reduce heat and simmer uncovered for about 30 minutes, until beef and potatoes are tender.
Stir in milk and heavy cream. Add peas and simmer for another 5–7 minutes until everything is heated through and the soup is thick and creamy.
Ladle the soup into bowls and serve with puff pastry, crescent rolls, or warm biscuits for that classic pot pie finish.