Preheat oven to 300f and make enough room to fit a Dutch oven.

Heat a large Dutch oven to medium heat with 2 tablespoons of olive oil. Season the short ribs with salt and pepper on both sides and sear in the Dutch oven until browned on all sides. Work in batches until finished. Add 5 cups of water to the pot and turn the heat to high. Scrape all of the browned bits off the bottom of the pot then turn the heat off and return all the beef to the pot. Cover with a tight-fitting lid and braise in the oven until fork tender (about 2 ½ hours).

Remove the beef from the pot and pour all of the liquid into a large measuring cup. Reserve 3 cups of the beef liquid for later. Separate the fat that rises to the top with a ladle and place it into a bowl for later.

Once the beef is cool enough to handle break it down by shredding or chopping it into chunks while removing any large pieces of fat.

Fill a stockpot with salted water (roughly 2 tablespoons of kosher salt per gallon). Add the chunks of potatoes to the pot and bring to a boil. Once boiling, turn the heat to medium and partially cover with the lid. Cook the potatoes until fork tender, then drain in a colander.

Rice the potatoes (can also use a potato masher) in a large bowl. Combine with the milk, melted butter, and half the grated cheddar cheese. Taste the potatoes and season well with salt and pepper to taste. Once satisfied, mix the egg yolks into the potatoes.

Preheat oven to 400f.

Heat a large pan to medium with 4 tablespoons of the reserved fat from above. Add the carrots, onions, and celery along with a pinch of salt. Saute until the veggies are very soft (about 10-12 minutes) then add the garlic and cook for another 1-2 minutes.

Add the tomato paste, stir, and cook for 3 minutes. Next, add the dry red wine and turn the heat to high. With a wooden spoon, scrape the bottom of the pot to remove any browned bits. Cook until the liquid has almost completely evaporated (about 3-4 minutes).

Turn the heat down to medium and mix in the flour, cooking until all the white specks disappear. Add the reserved beef liquid, thyme, rosemary, peas, and Worcestershire sauce. Bring to a boil. Once boiling, lower the heat to a simmer and add mix in all of the beef. Cook until the liquid has reduced by half.

Taste test the filling and season well with salt and pepper. Add more herbs if you like.

Add the filling to a 9x13" baking dish. Spread the mashed potatoes on the top (can also pipe with a pastry bag and star tip) and with a fork or spoon fluff the potatoes making mounds or points. Sprinkle the remaining cheddar cheese all over the top.

Bake for 25 minutes in the center of the oven. Move the dish towards the top of the oven and broil for 2-3 minutes or until well browned but not burnt. Watch carefully! Let the cottage pie sit for 10-15 minutes before eating so that it can settle. Enjoy!