Braise the short ribs following the linked recipe. When cool enough to handle, remove bones from the short ribs and discard. Shred meat using two forks, discarding any large pieces of fat or gristle. You should have about 3-½ cups of meat.

Follow the instructions in the short rib recipe to defat and reduce the braising liquid to 2-½ cups. Thicken the gravy by mixing together 2 tablespoons of cornstarch and 2 tablespoons cool water in a small bowl (a "slurry"). Stir the slurry into to the simmering liquid a little at a time, letting it bubble and thicken, until a rich gravy forms that coats the back of a spoon.

Heat 1 tablespoon oil in a nonstick skillet over medium-high heat. Add mushrooms with a pinch of salt and pepper. Sauté until released liquid is evaporated and mushrooms are lightly-browned. Set aside.

Heat an additional tablespoon of oil in the skillet. Sauté carrots and cippolini onions with a few pinches each of salt and pepper until vegetables are just crisp-tender and lightly-golden on the edges.

Boil cubed potatoes in lightly-salted water until soft (or cook in an electric pressure cooker according to your manufacturer's directions). Drain well and mash, or press through a potato ricer, into a large bowl.

Stir in melted butter, 1-½ cups shredded cheese, milk/half and half, and salt and pepper to taste (I use about 1-½ teaspoons salt, depending on the saltiness of the cheese, and ½ teaspoon pepper). Add egg yolks and stir until smooth. Keep warm until ready to use.

Preheat oven to 375 degrees F.

Add the shredded short rib meat to the gravy. Stir in the sautéed mushrooms, carrots, onions, frozen peas, and thyme leaves. Season to taste with salt and pepper.

Transfer the filling to a 3-quart oval baking dish, leaving enough room on top for the potatoes.

Spoon potatoes onto cottage pie filling, or pipe them with a pastry bag fitted with a large star tip. Be sure to "seal" the edges of the dish with potatoes to help keep the gravy from bubbling over. If you used a spoon instead of piping, make decorative swirls in the potatoes with a fork. Sprinkle with remaining ¼ cup shredded cheese.

Place dish on a foil-lined baking sheet (important: the pie will likely bubble over, despite your best sealing efforts!). Bake 35-40 minutes, until the filling is bubbling and the potatoes are golden brown. Let stand 15 minutes before serving.