Meanwhile, start the sauce. Heat canola oil and butter in large saucepan over medium heat and add the mushroom and onion. Stir occasionally, until browned, about 7–8 minutes. Stir in the carrot. Sprinkle with the flour and stir well. Stir in broth, wine, brandy, tomato paste, and thyme and bring to a boil. As soon as it boils, reduce to low heat and simmer until lightly thickened, about 10 minutes, checking periodically to make sure it does not dry. Add a couple of tablespoons of water if needed.