Preheat your oven to 350 degrees F and set your rack to the middle position. 

Put the potatoes in a large pot of salted water to cover (salty like the sea). Bring to boil then add 2 teaspoons of salt and reduce the heat and simmer for 20 minutes, until the potatoes are very tender. Drain. Pass the potatoes through a food mill or a ricer into a large mixing bowl. OR place them into a large mixing bowl/bowl of a stand mixer fitted with the whisk attachment and mix just until smooth. Set aside for now. 

Meanwhile, in a separate medium to large saucepan set over medium to med-high heat, add the olive oil, butter, garlic powder, and about ½ tsp salt. When the butter has melted, add the flour and whisk into a paste. Cook the paste for about 2 minutes (don’t let it brown). 

Whisk in the milk, ensuring that you mix until things are nice and smooth. Let the sauce come up to a bubble (it will thicken dramatically) mixture is smooth. Stir in the cheese and taste for seasoning – season your white sauce with salt and pepper as needed. Remember, erring on the side of saltiness is good here, as this is going to flavor all of the potatoes. Be generous! I usually use at least 2 tsp of salt and at least 1 tsp pepper. 

Turn off the heat and then add the cheese, stirring to combine. Add a little of this cheese sauce into your beaten eggs, to temper them. Then, pour the eggs into the cheese sauce (this little two-step will keep them from scrambling). Stir. 

Pour ¾ of this creamy, cheesy sauce into the potatoes, along with the olive oil, stirring to get everything well mixed. Taste and add more salt and pepper, as needed. Transfer this potato mixture to a 9 by 13-inch baking dish (or something comparable) that has been sprayed with non-stick spray (or buttered). Pour the remaining ¼ of the cream sauce over the top of your potatoes, spreading it out to cover as much of the surface as you can. 

Bake for 25 to 30 minutes, or until hot and a little bit bubbly all the way through and the sauce on top has set. Sprinkle with chives before serving, if desired.