Place the peeled and cut potatoes into a large pot and cover with cold water by about 1 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. Drain well.
While the potatoes cook, heat olive oil in a large skillet over medium heat.
Add the diced onion and cook until softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Add the ground beef to the skillet, breaking it up with a spoon. Cook until browned and cooked through, about 8-10 minutes.
Season the beef mixture with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Stir to combine and remove from heat.
In a large bowl, mash the drained potatoes with a potato masher until mostly smooth.
Add the butter, milk, sour cream, and remaining 1/4 teaspoon salt and 1/4 teaspoon black pepper to the potatoes.
Mix well until the mashed potatoes are creamy and smooth.
Serve the ground beef mixture alongside the mashed potatoes.