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 a Dutch oven or stock pot 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 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 aside. Add the carrots, 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, 1 minute.
Add 1 cup of the broth and scrape the bottom of the pan to lift any brown bits. Add the thyme, rosemary, bay leaves and short ribs. Top with the remaining broth, bring the liquid to a steady simmer. Cover with a lid, reduce the heat to low and cook until the meat is fork-tender, around 2.5 hours.
Transfer the short ribs and carrots to a tray and discard the bay leaves, thyme and rosemary. Using an immersion blender, blend the remaining liquid until smooth. Return the short ribs and carrots and cook until the meat is falling off the bone, around 30 more minutes. Taste the sauce for seasoning and adjust with salt and pepper as desired.
Serve the short ribs, gravy and carrots over a bed of mashed potatoes, sweet potatoes, or cauliflower purée.