Preheat oven to 325 degrees. Heat oil in a dutch oven over medium-high heat. Liberally salt and pepper the ribs and then brown them briefly on all sides, working in batches. Remove from pan and set aside.
Add the onions, carrots, and celery to the pan and cook until onions are lightly browned. Stir in 1 1/2 tbsp tapioca and tomato paste and mix until very well combined. Add the wine and garlic, increase heat to high, and bring to a boil. Once boiling, reduce heat to medium and simmer for 25 minutes.
Add beef broth and all herbs, bring back to a boil over high heat, cover and move to the oven. Cook for 2 1/2 hours, or until bones slide right out.
Remove short ribs and pour sauce through a strainer. Discard veggies (or save them to make bone broth later!), and spoon fat layer from remaining sauce. Pour the sauce back into the dutch oven, add another 1 tbsp of tapioca and the dijon mustard, and liberally season with salt and pepper. Bring to a boil, whisking often, and cook until the sauce has thickened a bit and reduced by half. Serve spooned over the short ribs.