With gentle heat and a lot of time, short ribs become incredibly luxurious, with a melt-in-your-mouth tenderness. This recipe's secret ingredient is a high-quality root beer—one brewed with real ingredients, not artificial flavors—that adds complex, herbal notes to the braising sauce.
Dice the onions, celery, and carrots; the pieces should be about the same size. Smash the garlic cloves. Peel 4 long strips of orange rind. Set everything aside.
Preheat oven to 325 degrees F. Place short ribs on a rimmed baking sheet lined with parchment paper and season all over with salt and pepper. In a large, heavy-bottomed pot with a lid, heat oil over high heat. Place short ribs in an even layer, without overcrowding (you might need to work in batches). Brown on each side, about 8 minutes total. Transfer browned ribs to a baking sheet.
Reduce heat under the pot to medium. Add the diced onions, celery, carrots (a combination known as a mirepoix) and garlic to the drippings. Use a wooden spoon to stir, loosening the brown bits (fond) on the bottom of the pan. Then, sweat the vegetables until onions are translucent and have no color, 4–5 minutes. Stir in the tomato paste and cook to slightly caramelize, 2–3 minutes. Meanwhile, pick thyme leaves from stems and thinly slice orange strips horizontally. Add 2 cups chicken stock, followed by thyme leaves, orange peel, Worcestershire, bay leaves, and root beer. Tuck short ribs into root beer mixture, then add 2 more cups chicken stock, just to cover; it’s fine if some ribs are showing, since they’ll shrink as they cook. Bring to a simmer; then cover and place in the oven for 4–4½ hours.
Check ribs after 4 hours; the meat should be very tender and pulling away from the bone. (If it needs more time, return to oven and check again after 30 minutes.) Use a strainer or slotted spoon to transfer the ribs to a wire rack fitted over a rimmed baking sheet. Strain braising liquid through a large strainer or chinois into a clean skillet. Bring strained liquid to a gentle simmer; spoon away and discard the fat from the edges of the pan. When most of the fat has been removed, bring to a boil to reduce slightly, 3-4 minutes.
Assembly: Gently place the short ribs back into the sauce and baste, to warm. Plate the ribs, ladle sauce over the top, and garnish with fresh parsley. Serve immediately.