Preheat oven to 425 degrees F.
Line a baking sheet with parchment paper, grease it with 1 tablespoon butter or oil and set it aside.
Add potatoes to a large pot and cover with cold water, over medium heat. Season with some salt and bring it to a boil.
Reduce heat to medium-low, cover the pot with a lid and simmer until the potatoes are very tender about 15 - 20 minutes. Transfer to a colander and drain potatoes very well.
Add 3 tablespoons of butter to a small saucepan and melt it over medium heat, once melted add garlic and saute until lightly golden, about 1 - 2 minutes.
Remove saucepan from heat, and stir in the half and half then pour the mixture into a small bowl, this is to avoid burning the garlic, set aside.
Transfer the drained potatoes into a large mixing bowl. Mash them until there are no longer any lumps.
Stir in parmesan cheese and the butter garlic mixture. Add nutmeg and season them with salt and pepper.
Let the mixture cool a few minutes, and then quickly stir in the egg yolks one at a time using a wooden spoon.
If the mixture is very thick, add 1 tablespoon half and half.
Transfer mixture to a large piping bag fitted with a large star tip. Pipe the potatoes onto the prepared baking sheet, make 12-16 mounds spaced evenly apart, being about 2 1/2-inches wide by 2 1/2-inches tall.
Gently brush them with the remaining 2 tablespoons of melted butter.
Bake in the preheated oven until golden brown, about 17-20 minutes.
Serve immediately garnished with parsley and grated parmesan cheese.