Preheat your oven to 400°F (200°C).
In a mixing bowl, combine the ground beef, breadcrumbs, Parmesan cheese, minced garlic, egg, salt, pepper, and parsley. Mix until just combined, being careful not to overwork the mixture.
Form the mixture into meatballs, about 1.5 inches in diameter, and place them on a baking sheet. Bake in the preheated oven for 15-20 minutes, or until they are browned and cooked through.
While the meatballs are baking, prepare the mashed potatoes. In a pot, boil the diced potatoes in salted water until tender, about 15 minutes. Drain and return to the pot.
Mash the potatoes with butter, then add milk until creamy. Season with salt and pepper to taste. Keep warm.
For the garlic butter sauce, heat the butter in a skillet over medium heat. Add the minced garlic and red pepper flakes (if using) and sauté for 1-2 minutes until fragrant but not burned.
Once the meatballs are done, transfer them to the skillet with the garlic butter sauce. Toss gently to coat the meatballs in the sauce.
To serve, place a generous portion of creamy mashed potatoes on each plate, top with garlic butter meatballs, and garnish with fresh parsley.