Place the peeled and quartered potatoes into a large pot and cover with cold water. Add a pinch of salt and bring to a boil over high heat.
Reduce heat to medium and simmer the potatoes for 15-20 minutes or until tender when pierced with a fork.
While the potatoes cook, heat olive oil in a large skillet over medium-high heat.
Add diced onions and cook for 3-4 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add ground beef to the skillet and cook, breaking it apart with a spoon, until browned and cooked through, about 8-10 minutes.
Drain excess fat from the skillet if necessary.
Stir in diced carrots and celery, and cook for 5 minutes until slightly softened.
Add tomato paste, dried thyme, dried rosemary, salt, and black pepper. Stir to combine.
Pour in beef broth and bring the mixture to a simmer. Cover and cook for 10 minutes, stirring occasionally.
Add frozen peas to the skillet and cook for an additional 3 minutes until heated through.
Drain the cooked potatoes and return them to the pot.
Add butter and milk to the potatoes and mash until smooth and creamy. Season with salt and pepper to taste.
Serve the ground beef mixture over a bed of mashed potatoes.