In a large pot, pour in enough water to cover potatoes by 1"; generously season with salt. Cover pot and bring to a boil, then uncover and continue to boil until potatoes are very soft and easily pierced with a knife, 10 to 15 minutes. Drain and return potatoes to pot. Cook over medium heat, stirring, until dry and starting to break down, about 2 minutes. Remove from heat.
Meanwhile, in a small saucepan over low heat, cook milk, butter, garlic, and a pinch of salt and pepper. Cover and let butter slowly melt and garlic steep while potatoes cook, about 30 minutes. Discard garlic.
Pour milk mixture into pot with potatoes. Using a handheld mixer on medium speed, beat potatoes until smooth. Add three-quarters of feta; season with salt and pepper.
Transfer potatoes to a serving bowl. Top with a few pats of butter, parsley, and remaining feta.
