Season short ribs with salt and pepper. In a Dutch oven or deep oven-proof pot, brown ribs on all sides over medium-high heat in canola oil.
Remove beef from pan. Remove excess fat, leaving about 3 tablespoons. Add vegetables and cook until starting to brown. Sprinkle with flour and stir with a wooden spoon to cook the flour. Add tomato paste, continue to stir.
Deglaze with red wine. Add stock, herbs, and garlic. Bring back to a boil. Add ribs plus accumulated juices.
Cover pot and cook at 350°F for 2 to 2 1/2 hours until ribs are very tender.
Let the pot cool slightly then remove ribs to a platter. Let ribs come to room temperature, then cover and refrigerate overnight.
Strain the sauce. Discard solids. Let cool to room temperature then cover and refrigerate overnight.
The next day, remove most of the congealed fat from the top of the sauce. Bring sauce to a boil and reduce to thicken. Add a corn starch slurry to get a thicker sauce if desired. Season to taste with salt and pepper. Gently reheat ribs in the sauce.
Note: If serving small tasting portions, slice cold meat from the bones into bite-sized pieces then reheat in the sauce.