Heat the olive oil in a large pot or Dutch oven over medium heat.
Add the diced onion and sauté for 3-4 minutes until translucent.
Stir in the minced garlic, diced carrots, and celery. Cook for an additional 5 minutes until the vegetables start to soften.
Add the ground beef or lamb to the pot. Cook, breaking it up with a spoon, until browned (about 5-7 minutes).
Pour in the beef broth and bring the mixture to a boil.
Stir in the frozen peas, tomato paste, Worcestershire sauce, thyme, and rosemary. Reduce the heat and let it simmer for 15 minutes.
Season the soup with salt and pepper to taste.
To serve, ladle the soup into bowls and top each serving with a generous scoop of mashed potatoes.