Pat dry short ribs.
Generously apply kosher salt and freshly cracked pepper on all sides of the ribs.
Heat a couple tablespoons of vegetable oil in your Dutch oven until it sizzles when you drop a drop of water into it.
Sear the ribs on all sides (don’t forget the “corners”) for about two minutes per side or until it’s nicely browned. Don’t move them around while searing. And please don’t crowd the pan.
When they’re all nice and brown, remove from the pan and set aside.
Preheat oven to 300°F.
If your ribs were very fatty, remove some of the liquid and leave about 2 tablespoons remaining in the pot.
Add the two halves of garlic, cut side down, and let them sizzle undisturbed for 1 to 2 minutes.
Add chopped vegetables and ½ teaspoon each of kosher salt and pepper.
Cook for 5 minutes while stirring occasionally. Adjust the heat so nothing starts to burn.
Add a tablespoon of tomato paste and stir so that all vegetables will get lightly coated and caramelized, about 2 minutes.
Add ½ bottle red wine and cook for about 2 minutes (now it’s time to use a wooden spoon and scrape all the delicious morsels from the bottom of the pan).
Add the seared ribs back into the Dutch oven, top with all the herb sprigs, and add beef stock. Add enough liquid so the ribs are just about covered.
Place the lid on top and transfer it to the oven, leaving the lid on throughout the entire time it’s in the oven.
Patiently wait for 3 to 3-½ hours.