Place the diced potatoes in a large pot and cover with cold water. Add 1/2 teaspoon salt and bring to a boil over high heat. Reduce heat to medium and simmer until potatoes are tender, about 15 minutes.
While the potatoes cook, heat olive oil in a large skillet over medium heat. Add diced onion and sauté for 3-4 minutes until softened.
Add minced garlic to the skillet and cook for 1 minute until fragrant.
Add ground beef to the skillet with onions and garlic. Cook, breaking up the meat with a spoon, until browned and cooked through, about 7-8 minutes. Drain excess fat if necessary.
Stir in diced carrots, frozen peas, dried thyme, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Cook for an additional 5 minutes until vegetables are tender.
Drain the cooked potatoes and return them to the pot. Add butter, milk, and remaining 1/2 teaspoon salt and 1/4 teaspoon black pepper. Mash until smooth and creamy.
To serve, plate a generous scoop of mashed potatoes topped with the seasoned ground beef and vegetable mixture.