Cook the potatoes: Transfer the potatoes, the garlic, and the onion to a pot filled with cold water and bring to a boil. Reduce heat to a gentle simmer and cook until the potatoes are fork tender.
Warm the milk: transfer the milk, the butter, the olive oil, the salt and the nutmeg to a small pot and heat until the butter is melted and the mixture is very warm. Keep it warm until you add it to the potatoes.
Drain and Mash: When the potatoes are cooked, drain them very well and discard the onion and the garlic cloves. Return the pot over the heat and cook stirring gently for 2 minutes until all the moisture is gone.Remove the pot from the heat and mash them using a potato masher, or a ricer. You can also pass them through a large sieve, pressing them with the back of a wooden spatula.
Add all of the grated cheese and then the milk mixture gradually folding with a spatula until you get a creamy, silky consistency (you may not need all the milk). Taste and adjust the salt.
Serve with chopped chives or green onions.
Notes
For 2.2 pounds (1 kg) peeled potatoes you will need approximately 2.9 pounds (1.3 kg) unpeeled potatoes.For a more intense potato flavor you can cook the potatoes with the skin on. Use a towel to help you peel them while they’re still hot.The exact quantity of the milk you'll need depends on the moisture of the potatoes. Keep adding milk until the mashed potatoes reach the texture of your preference.For richer taste use half and half cream or replace half of the milk with heavy cream.Instead of chives you can also use green onions.