Generously season the short ribs on all sides with salt and pepper; set aside about 15 minutes.
In a baking pan over medium-high heat, add oil and when hot, add the seasoned meat, fat side down, and brown on all sides including the ends, about 7 to 10 minutes. Transfer the short ribs to a plate and set aside.
Reduce the heat to medium, add onions and carrots; sauté for 5 minutes. Halfway through cooking, add clarified butter.
Add garlic and sauté for 30 seconds. Add tomato paste and stir to coat.
Pour in the wine, stir to deglaze and bring to a boil. Cook until the liquid is reduced by half, about 10 minutes.
Preheat oven to 300ºF/150ºF
Add the beef broth, thyme, rosemary, brown sugar, cayenne pepper, salt and black pepper; stir well.
Return the meat to the pan, bone side up, including any accumulated juices. Spoon the sauce over the ribs to prevent them from drying out and bring the mixture to a simmer.
Cover the pan tightly with foil and transfer it to the preheated oven. Cook for 1:30 hours until the ribs are fork-tender or the internal temperature reaches between 165ºF to 170ºF.
Remove from the heat and transfer the meat to a plate while making the gravy.
Remove and discard the sprigs including any bones left in the pan. Skim off any excess fat and discard it.
Bring the mixture to a boil and add cornstarch mixture; stir until it thickens.
To serve, place ribs along with carrots on mashed potatoes or polenta and spoon the gravy on top.