In a heavy ovenproof pot, add enough oil to cover the bottom about ¼" (5 mm).
Put some flour on a plate and dredge the short ribs (or your choice of meat) on all sides and shake off the excess.
When the oil is hot, add the ribs/meat and brown on all sides—you may have to do this in batches so as not to crowd the pan and steam instead of sear. You want to form a nice crust on the beef meat. There is lots of flavor in this.
Remove the ribs/meat and drain on paper towel.
Preheat the oven to very low 250°.
Drain off any remaining oil, and wipe pot clean.
Add a little canola oil to coat the bottom of the pot, add half the onions and cook over medium heat until the onions have softened.
Add a sprinkle of salt.
Add half the carrots and all the celery (refrigerate the onions and carrots for use later). Cook for 5 minutes—the longer you cook the vegetables and they caramelize you develop flavor—so you can brown them up.
Add tomato paste and stir around to heat through.
Add the wine (or stock/water if using)—3 cups is just about the entire bottle and if it’s too early to enjoy a glass then you can add the entire bottle!
Add the garlic (its ok for the cloves to be unpeeled but remove the outer layers) Add the honey and peppercorns. Add the bay leaves, and season with a sprinkle of salt.
Place the ribs/meat in the pot (its ok if they go on top of each other now). Bring to a simmer.
Cover pot with the lid ajar or make a parchment lid to fit. Place in the oven and cook for 4 hours.
Remove the pot from the oven and allow cooling. Remove ribs meat and place on a plate and cover with plastic wrap and refrigerate.
Strain the braising liquid and allow chilling - then removing the congealed fat.
Sear mushrooms by placing them in a hot dry sauté or frying pan and cook for a minute or two each side, while pressing down with the spatula.
Melt butter in your braising pot.
Add the remaining onions and carrots and sauté for 5 minutes. Add ribs and mushrooms. Add the reserved braising liquid.
Bring to a simmer. Cover and cook over medium-low heat until carrots a fork tender.
For the Gremolata, stir together the parsley, garlic and lemon zest. Don’t skip this part—the Gremolata adds so much to this dish. You can also use orange zest too!
Serve ribs with mashed potato, buttered egg noodles or polenta—garnish with the Gremolata.