Liberally season the short ribs with salt and pepper on all sides. Allow them to come to room temperature – the resting time should take about 30 minutes.
Preheat oven to 400 degrees.
On the stovetop, preheat a heavy-bottomed saucepan or roasting pan to medium-high heat.
Add olive oil to the pan.
Using tongs, sear all 4 sides of the short ribs until browned, about 2-3 minutes per side. Once seared, set aside on plate or baking sheet.
In the same cooking pan you just used to sear the short ribs, add the onion, carrots, celery, and garlic. Cook for 4-5 minutes.
Add both the tomato paste and dijon mustard and stir well. Cook 2-3 minutes or until the tomato paste starts to brown.
Deglaze the pan with red wine (pour the wine into the vegetable/tomato mixture) and cook for 2-3 minutes.
Add the diced tomatoes and the broth; cook for additional 2-3 minutes. Add short ribs to the pan. Add the fresh thyme sprigs.
Cover with foil or lid and place in oven for at least 4 hours, until the meat is tender and falling off the bone.
CAREFULLY remove everything from the oven. Use mitts to remove the tin foil/covering from the pan. Taste and adjust seasoning as desired.