Sprinkle the short ribs with salt and pepper. Melt the butter in a large, wide pot over medium-high heat. Working in two batches, cook the short ribs until browned on all sides, about 6 minutes per batch. Transfer to a rimmed baking sheet.
Add the celery, carrots and onions to the pot and saute until beginning to soften and brown, about 5 minutes. Add the red wine, beef stock, sherry, garlic, bay leaves and thyme sprigs. Bring to a boil, scraping up any browned bits on the bottom of the pot. Add salt and pepper to taste. Return the browned short ribs to the pot in a single layer, propping them up on their sides. Cover the pot, reduce the heat to medium low and simmer for 1 hour.
Turn the short ribs with tongs and continue simmering, covered, until the short ribs are tender and the sauce is very thick, up to 12 hours, turning occasionally and rearranging the ribs in the pot to prevent sticking. When the meat is beginning to fall off the bone, turn off the heat, uncover the pot and let cool for 30 minutes.
Transfer the short ribs to a work surface and separate the meat from the bones; discard the bones. Cut the meat into 3/4- to 1-inch pieces, trimming any fat. Discard the bay leaves and thyme sprigs from the pot and skim the fat from the sauce. Return the meat to the pot and keep warm.
To assemble: Place the toasted English muffin halves on plates. Top each muffin half with 6 ounces of short ribs and a poached egg, then cover with hollandaise and garnish with sauteed arugula.
The short ribs can be made up to 2 days ahead. Reheat them in a 300-degree oven for 15 minutes prior to serving.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.
Recipe courtesy of Wilma & Frieda, Palm Springs, CA