Put diced potatoes in a large pot. Cover with water and bring to a boil over high heat. Reduce heat and simmer until potatoes are fork tender, about 15 minutes. Drain and transfer to a stand mixer fitted with a whisk attachment. Add in melted butter and beat slowly until mostly mashed. Add in sour cream, 1/4 cup milk, cheese, salt, and black pepper. Continue beating until it reaches desired consistency, adding remaining 1/4 cup of milk if necessary. Use a rubber spatula to stir in half of the green onions and bacon.