To marinate the beef, place the cubes in a large glass or stainless steel bowl. Add the wine, carrot, celery, and onion. Cover and refrigerate for at least 2 hours or overnight.
Line both a baking sheet and a large plate with paper towels.
Remove the beef from the marinade and transfer to the prepared baking sheet. Pat the meat dry with paper towels. Strain the marinade, reserving separately both the vegetables and the liquid.
To cook the beef, heat a large skillet over medium-high heat. Add the bacon and cook until the fat is rendered and the bacon is crisp, about 5 minutes. Remove the bacon with a slotted spoon to the prepared plate to drain. Pour off all but 1 tablespoon of the bacon fat from the pan. Decrease the heat to medium, add 2 tablespoons of the canola oil and heat until shimmering.
Season the beef with salt and pepper. Sear the beef in two or three batches without crowding until nicely browned on all sides, about 5 minutes; transfer to the prepared baking sheet when done. (For ease of removal later, wrap the beef in cheesecloth and tie with cotton butcherâs twine.) Set aside.
Add the reserved vegetables from the marinade and cook until they start to color, 5 to 7 minutes. Sprinkle on the flour and toss again to lightly coat. Cook, stirring constantly, until the flour turns brown, 2 to 3 minutes.
Transfer the vegetables and cheesecloth bound package of beef to the insert of a slow cooker. Add the reserved marinade liquid and enough stock to barely cover the meat. Add the bouquet garni, tomato paste, and garlic. Seal with the lid. Cook on high heat for 3 to 4 hours or low for 6 to 8 hours.
Remove the bouquet garni and discard. Transfer the cheesecloth bound packet of beef or remove the individual pieces with a slotted spoon to a bowl. Remove and discard the cheesecloth.
Using an immersion blender, puree the sauce and vegetables remaining in the insert until smooth. (Or, once the beef is removed, ladle the sauce and vegetables into a blender and puree until smooth a little at a time.) Return the reserved beef to the sauce. Add the mushrooms and continue to cook until tender, about 30 minutes. Taste and adjust for seasoning with salt and pepper. Serve piping hot with noodles, potatoes, or rice. Or, better yet, reheat and serve the next day.