Take your short ribs out of the refrigerator about an hour before cooking. Season your mean with salt and pepper.
Preheat oven to 330 degrees Fahrenheit.
Heat a few teaspoons of oil on medium heat. In batches, cook the short ribs for about 2 minutes per side. Do not crowd the pot. Set the short ribs on the side.
In the same dish, add a little more oil (if needed). Add the onions and carrots. Cook until the onions and carrots begin to soften and caramelize.
Stir in the garlic. Cook for an additional minute.
Add the celery and cook for about 30 more seconds.
Pour in the wine. Raise the heat to medium-high and cook until the wine evaporates by about half.
Lower the heat back to medium. Stir in the tomato paste.
Add the parsley.
Pour in the chicken stock.
Return the short ribs back into the pot.
Transfer the short ribs to the oven. Cover and bake for about 3 hours and 30 minutes. Uncover after 2 hours into the baking process.
Skim the fat off the top of the dish.