Preheat the oven to 375F.
Preheat your dutch oven over medium-high then add the ground beef, season with salt and allow to sit undisturbed until it easily releases from the pan, 4-5 minutes. Add the carrots and shallots then begin breaking up the meat and stirring until the mince is fully cooked, an additional 4-5 minutes. Add the garlic and stir for one minute.Note: Depending on the fat content of your ground beef you may need to remove excess fat from the pan. Add the tomato paste and stir constantly until it becomes a deep red and starts to stick to the bottom of the pan. Deglaze with the red wine and cook until it has reduced completely.
Add the beef broth and thyme then season with salt and bring to a simmer, stirring occasionally until reduced to about 1/2-3/4 cup. Meanwhile, mash together the flour and butter until it becomes a paste, this is called beurre manie. When the broth is finished reducing add the beurre manie and chopped parsley then stir until it has completely mixed in and the sauce is thick and glossy. If using a baking dish transfer the meat mixture to the baking dish now.