1. Preheat the oven to 300 degrees F.
2. Heat the olive oil in a large dutch oven style pot over medium high heat.
3. Generously season the short ribs on both sides with salt and pepper.
4. Place half of the short ribs in a single layer in the pot. Cook for 4-5 minutes per side or until golden brown. Repeat the process with the remaining meat.
5. Remove the meat from the pan, and cover with foil to keep warm.
6. Add the onions and carrot to the pan. Season the vegetables with salt and pepper to taste. Cook for 4-5 minutes or until just tender and starting to brown.
7. Add the garlic and cook for one more minute, stirring constantly.
8. Add the short ribs, thyme, bay leaf, beef broth and root beer to the pot. Bring to a simmer. Cover and place the pot in the oven.
9. Bake for 3-4 hours, or until meat is tender.
10. Remove the pot from the oven. Take the ribs out of the pot and cover to keep warm. Discard the bay leaf and thyme sprigs. Skim any fat off the surface of the liquid.
11. Place the pot on the stove and bring to a simmer over medium heat. Mix the cornstarch with 2 tablespoons of cold water and add it to the pot. Bring to a boil and cook for one minute or until thickened.
12. Add the ribs back to the pot and spoon the sauce over the top. Add salt and pepper to taste if desired. Garnish with thyme sprigs, then serve.