In a large pot, heat the olive oil over medium heat. Add the diced onion and cook until translucent, about 5 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.
Add the ground beef or lamb to the pot, breaking it apart with a spoon. Cook until browned, about 6-8 minutes. Drain excess fat if necessary.
Stir in the diced carrots and celery, cooking for another 5 minutes until they begin to soften.
Add the frozen peas, beef broth, tomato paste, Worcestershire sauce, thyme, rosemary, salt, and pepper. Bring the mixture to a boil, then reduce the heat and let it simmer for 20 minutes, stirring occasionally.
Once the soup has thickened slightly, ladle it into bowls and top each serving with a generous scoop of mashed potatoes.
Garnish with chopped fresh parsley before serving.