Place the peeled and cubed potatoes in a large pot and cover with cold water by about an inch.
Add 1/2 teaspoon salt to the water and bring to a boil over high heat.
Reduce heat to medium and simmer the potatoes until tender, about 15-20 minutes. Test by piercing with a fork; potatoes should break apart easily.
While the potatoes cook, heat olive oil in a large skillet over medium heat.
Add the chopped onion and cook until translucent, about 3-4 minutes.
Add minced garlic and cook for an additional 1 minute until fragrant.
Add ground beef to the skillet and cook, breaking it apart with a spatula, until browned and cooked through, about 7-8 minutes.
Season the beef mixture with 1/2 teaspoon salt, 1/2 teaspoon black pepper, dried parsley, and dried thyme. Stir to combine and cook for another 2 minutes. Remove from heat and set aside.
Drain the cooked potatoes and return them to the pot.
Add 3 tablespoons butter, whole milk, and remaining 1/2 teaspoon salt and 1/2 teaspoon black pepper to the potatoes.
Mash the potatoes using a potato masher or hand mixer until smooth and creamy.
Serve the mashed potatoes topped with the seasoned ground beef mixture.