Combine flour, paprika, cayenne pepper and black pepper in a bowl. Add the short ribs, coating them lightly in the flour mixture.
In a large Dutch oven or deep oven-proof pot over medium heat, melt butter until golden. Add the ribs, shaking off any excess flour. Sear the meat until brown, moving the ribs around covering them with the butter. In the same pot, saute the bacon for 2 to 3 minutes then add the onions, shallots, mushrooms, celery and carrots and saute until golden. Deglaze the pan with the red wine, adding a little at a time. Let reduce over high heat for 1 minute. Add the rest of the wine and beef stock, and bring to a simmer. Once the liquid has come to a simmer, cover, and cook in the oven for 2 to 3 hours. Taste and adjust seasoning.