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Line a sheet pan with a wire rack. Liberally season all sides of the short ribs and place them bone side-up the rack. Refrigerate, uncovered, 1 hour to overnight. Remove from fridge and let the meat come to room temperature before cooking, around 1 hour.
Preheat oven to 375F.
Preheat a Dutch oven over medium heat for 5 minutes. Raise the heat to medium-high, add the avocado oil and heat the oil until shimmering. Pat the short ribs dry with paper towel and carefully add them to the pan. Cook until deeply browned on all sides, around 12 minutes total. If necessary, brown the meat in batches so as not to overcrowd the pan.
Transfer the short ribs a bowl and set them aside. Add the carrot, celery and onion. Season with a pinch of salt and cook, scraping the bottom of the pan with a wooden spoon, until slightly softened, around 3 minutes. Add the garlic and cook 60 seconds. Add the mushroom powder, if using, and cook, stirring 60 seconds. Add the tomato paste and cook, stirring to combine, 2 minutes.
Add 1/2 cup of the broth and scrape the bottom of the pan to lift any brown bits. Add another ½ cup of broth along with the thyme, rosemary and bay leaves. Stir to combine. Nestle in the short ribs, bone side-down, and bring the liquid to a steady simmer. Cover with a lid and transfer to the oven. Cook until the meat is falling off the bone and easily shredded with a fork, around 2.5 hours.
Discard the bay leaves, thyme and rosemary and arrange the short ribs and carrots on a serving platter. Place the pan back over medium heat and use a potato masher or the back of a wooden spoon to mash the vegetables until smooth and creamy. Deglaze the pan with the remaining stock and simmer, scraping any brown bits off the bottom of the pan, until combined, around 3 minutes.
Spoon the pan sauce over top of the short ribs, garnish with parsley and serve.