Begin by salting the duck leg quarters. Place them skin side down in a cold saucepan. Set over medium heat and render the fat until the skin is crispy. Remove the duck legs and drain excess fat.

Add brunoise celery, carrot, and onion to the saucepan. Season with a pinch of salt and sauté until translucent.

Add sliced garlic and sauté for 30 seconds. Stir in tomato paste until fond develops on the bottom of the pan.

Deglaze the pan with red wine, scraping up any browned bits. Add crushed tomatoes and chicken stock.

Return the duck legs to the pan, cover loosely, and bring to a light simmer. Transfer to a preheated oven at 325°F (160°C) for 2 hours or until very tender.

Remove from the oven, separate the duck meat from the bones, and shred the meat. Place shredded meat in a pot and ladle over enough sauce to cover. Reserve any leftover sauce.

Bring the pot to a light simmer, then stir in heavy whipping cream. Salt to taste.

Preheat oven to 400°F (200°C). Coat Yukon gold potatoes in olive oil and bake for 1 hour until tender. Let cool slightly, then slice in half and scoop out the insides.

Pass the potato through a potato ricer onto a cutting board, forming a large pile. Add egg yolks, salt, and start with ⅔ cup of flour. Fold in flour until combined, adding more as needed until the dough forms a cohesive mass. Do not overwork.

On a floured surface, roll the dough into a log. Cut into small sections and shape into gnocchi by rolling into small rods, then cutting into 1-inch pieces and pinching the sides to form pillow shapes. Place on a generously floured baking sheet.

In a pan, melt butter over medium-high heat. Cook gnocchi in salted boiling water until they float to the top, about 1-2 minutes. Remove with a slotted spoon and add cooked gnocchi to the butter, searing on both sides until crispy.

Once crispy, add a couple spoonfuls of duck ragu sauce to lightly coat each gnocchi. Add a small ladle of pasta water, then grate in a generous amount of Parmigiano Reggiano. Toss to combine.

Plate the gnocchi on a hot dish, topped with additional Parmigiano Reggiano. Serve and enjoy immediately.