Add 2 tablespoons of canola oil to a Dutch oven over medium-high heat, and allow to come to temperature. Pat the short ribs dry with a paper towel, drizzle with 1 tablespoon of canola oil, sprinkle with TAK Seasoning and rub to adhere.
Add the short ribs to the Dutch oven, taking care not to overcrowd the pot and sear in batches. Sear for 3-4 minutes on the first side, until browned and crusted. Turn and sear for 2-3 minutes more. Transfer the ribs to a plate and set aside.
Reduce the heat to medium-low and add the butter. Add the onions and sauté for 6 - 8 minutes until softened. Add the garlic, and sauté 1-2 minutes more. Sprinkle over flour, and stir until vegetables are coated.
Very slowly stream in the wine, stirring all the while. Add the beef broth, pepper, salt, thyme, and bay leaf to the pot and stir to combine. Add the short ribs back in, and increase the heat to medium-high. Allow the mixture to come to a rapid simmer. Add the mushrooms, and transfer to the oven, and cook for 3 hours.
Remove from the oven, skim off any unwanted fat/grease from the top (if desired), serve and enjoy.