Heat a large stock pot over medium-high heat and add canola oil. Season the short ribs with the salt and pepper then lightly coat them with the flour. Add the short ribs to the pot (you may need to do this in two batches) and sear until golden on all sides, about 1 minute per side. Remove the short ribs and add them to the slow cooker.
Add the mushrooms, onions, garlic, diced tomatoes, tomato sauce, paste, beef stock and red wine to the slow cooked with the ribs. Stir in the oregano and thyme. Stir as much as you can, then cook on low for 8 hours.
After 8 hours, remove the ribs with a pair of kitchen tongs (keep the sauce covered) and let them slightly cool until you can touch them. Remove the beef from the ribs and add it back to the slow cooker. Add in the brown sugar, salt, pepper, red pepper flakes and cheese. Stir well and cook for another hour on low heat. Remove the thyme sprigs.
Before serving, taste the sauce and season additionally if desired. You might need more salt and pepper. Don’t be afraid to add it! Serve over bucatini and top with extra cheese.