Start by seasoning your short ribs generously with salt and pepper. Heat the vegetable oil in a large, heavy pot over medium-high heat. Once hot, brown the short ribs on all sides, about 3-4 minutes per side. This step is crucial; it locks in the flavors and creates that delightful crust.

Remove the short ribs and set them aside. In the same pot, toss in the cremini mushrooms, cippolini onions, and carrots. Cook them until they soften and show a glimmer of color — roughly 7-9 minutes. Don’t rush this; the caramelization adds depth.

Now, return the short ribs to the pot and add a splash of stout beer. The liquid should cover about a third of the meat. Cover the pot, reduce the heat to low, and allow those ribs to braise for about 2-3 hours. The low and slow approach is key. Your kitchen will smell divine.

While the ribs are happily bubbling away, peel and chop the Yukon Gold potatoes. Boil them in salted water until fork-tender, about 15 minutes. Drain them well, and then mash away. Mix in the milk or half-and-half, melted butter, and half of the shredded cheese. Add a pinch of salt and pepper to taste, followed by the egg yolks. This will elevate the creaminess.

Once the short ribs are tender and the meat falls apart, shred or chop the meat. Combine it with the sautéed veggies, frozen peas, fresh thyme, Dijon mustard, parsley, and season with some more salt and pepper. Pour this filling into a baking dish, spreading it evenly. Cover with the fluffy mashed potatoes, smoothing the top. Sprinkle the remaining cheese on top for that irresistible crust.

Preheat your oven to 400°F. Bake the assembled pie for about 25-30 minutes until the top is golden brown. You want to give it that perfect crispiness while ensuring everything inside is piping hot.