Place the peeled, quartered potatoes in a medium pot and cover with at least an inch of cold water. Add 2 tablespoons salt and bring to a boil over medium-high heat. Cook until fork tender, about 10 minutes.

Drain the potatoes and transfer back to the pot. Set on the stove over medium heat to let any excess water cook off, shaking the pot a few times.

Rice the hot potatoes into a large bowl or press them through a box grater after cooling for about 10 minutes.

Add the butter and pepper to the potatoes and mix gently until the butter is melted. Set aside to cool to room temperature, about 1 hour.

Once cooled, add Parmesan cheese, egg yolks, and chives to the mashed potatoes. Mix gently until combined.

Scoop out golf ball-sized portions and roll each into a uniform ball. Place on a baking sheet.

Preheat oil in a medium saucepan to 350°F, ensuring it is at least 2 inches deep.

Add fine breadcrumbs to a plate. Whisk egg whites in a small bowl.

Dip each croquette into the egg whites, then into the breadcrumbs, coating thoroughly. Set back on the baking sheet.

Carefully add a few croquettes to the hot oil. Fry until golden brown all over, about 3 minutes.

Transfer fried croquettes to a baking sheet lined with paper towels and sprinkle lightly with salt.

Repeat breading and frying until all croquettes are cooked. Adjust oil levels as needed.