Season the meat beautifully with salt and black pepper, and lightly coat with as little olive oil as possible (about 1 tablespoon) allow to sit 10 minutes.
Optional Smoke: Set up the smoker to do an indirect smoke between 190 and 220 degrees. Once the smoker has settled, smoke the meat on indirect heat for 10-15 minutes (overdoing this will overwhelm the dish). Remove the meat.
Preheat oven to 350 degrees.
Heat 1 tablespoon of the olive oil in a large Dutch oven to medium high heat.
Sear the meat on all sides to a deep brown color. I recommend doing this in batches to give the pieces plenty of space.
Set the meat aside.
Add enough extra olive oil to do the rest of the cook that follows.
Cut the garlic button in half. Do not separate the cloves.
Sear the garlic flat side down on the oiled skillet for 2 minutes.
Add the tomato paste an cook it out by stirring in the oil making sure all gets exposed to the heat.
Add the ¾ bottle of red wine and the thyme.
Deglaze the bottom of the Dutch oven with the liquid.
Add the balsamic vinegar and simmer for a few minutes to blend flavors, then add the meat.
Pour in the beef (or chicken) stock until the meat is almost but not quite covered. Cover the pot and place into the oven.
Braise at 350 for 4 hours. You might want to check the liquid at about hour 3 but it really should be ok.
After the braising, remove from oven.
Remove the meat to rest. It should be glazed with beautiful brown coating.
Remove the liquid in the pot and strain out the garlic, thyme, and any other solid bits.
Transfer the liquid to a medium skillet or saucepan.
Add the oyster sauce, sriracha, and honey.
Reduce over medium heat until the sauce is thick and rich.
Plate the meat, cover with the sauce, serve!