Begin by placing your peeled and quartered Yukon Gold potatoes in a large pot. Cover them with cold water and add a generous pinch of salt. Bring to a boil over medium-high heat. Once boiling, reduce the heat to a simmer and cook for about 15-20 minutes, or until the potatoes are fork-tender.
Drain the potatoes and return them to the pot. Add the unsalted butter, salt, and pepper to taste. Mash the potatoes until smooth and creamy. Allow the mixture to cool slightly.
Once the mashed potatoes have cooled, stir in the egg yolks, grated Parmesan cheese, and chopped fresh parsley until well combined.
In a shallow dish, place the all-purpose flour. In another bowl, beat the egg for the egg wash. Prepare a platter lined with parchment paper for the formed croquettes. Take a small amount of the potato mixture and shape it into a log or oval, about 2 inches long. Roll each croquette in flour, dip it in the egg wash, and then coat with whole wheat breadcrumbs. Place them on the platter.
In a large frying pan, heat a generous amount of neutral oil over medium heat. Once the oil is hot, gently place a few croquettes in the pan. Fry for 3-4 minutes on each side, or until golden brown and crispy. Use a slotted spoon to transfer the croquettes to the prepared platter, allowing excess oil to drain.
Garnish the Potato Croquettes with additional chopped parsley before serving. Enjoy warm!
