Preheat the oven to 300°F.
Thoroughly season the short ribs with salt & pepper.
In a large skillet, heat the olive oil over medium-high.
Working in batches, sear the short ribs on all sides until deeply browned, 8 to 10 minutes per batch. Transfer the browned short ribs to a wide baking dish. Nestle the sprigs of thyme and sage in between and under the short ribs.
Measure ¼ cup of drippings from the skillet and save the remaining fat for another use. Pour the drippings back into the skillet over medium-high heat.
Add the mushrooms and season with salt & pepper. As the mushrooms release moisture, use a wooden spoon to scrape up any browned bits stuck to the bottom of the pan. Cook the mushrooms until they are golden brown, about 10 minutes. Transfer the mushrooms to the baking dish with the short ribs.
Reduce the heat to medium and add the garlic and onions. Season with salt and pepper.
Cook until the onion mixture is just softened, 4 to 5 minutes. Add the tomato paste and cook, stirring frequently, until it caramelizes slightly, 2 to 3 minutes.
Add the red wine and bring to a simmer. Cook until the wine has reduced slightly, about 7 minutes. Add the chicken stock and bring to a simmer. Pour the hot liquid over the meat. Add more chicken stock or water as needed to ensure most of the meat is submerged.
Cover and transfer to the oven. Bake until the short ribs are tender, 3½ to 4 hours.
Transfer the short ribs to a platter, skim the fat off the braising juices, and spoon over the short ribs.