Place lamb shanks with all marinade ingredients in a large ziplock bag. Let sit in fridge overnight (24 hours before use).
Preheat oven to 350.
Brush olive oil on all sides of lamb shanks. Season shanks with salt and pepper.
Heat a large oven proof roasting pan or dutch oven over HIGH heat. Add the shanks when the pot is hot and sear on all sides until golden brown, about 8-10 minutes (2 minutes per side). Remove shanks and set aside.
In the same pot, add the onion, carrots, and celery to the pan, season with salt and pepper, and cook until lightly golden brown over HIGH heat, 4-5 minutes. Add the wine and cook until reduced by half, about 2-3 minutes. Add the thyme, stock, and lamb shanks and bring to a boil. Cover, place in the oven, and braise until the meat is tender, about 2 - 2.5 hours.
Remove the shanks to a plate and tent loosely with foil. Stain the sauce through a finely meshed strainer and return liquid contents back to the pot and place over HIGH heat. Add the chiles (remove seeds unless you like a very spicy sauce) and brown sugar and cook, stirring occasionally, until reduced to sauce consistency (15-20 minutes - liquid should coat the back of a spoon). If after cooking down you would like a thicker sauce, mix flour with cold water in a measuring cup, then slowing whisk into sauce until reach desired consistency.
Add the vinegar to the sauce and cook 1 minute over HIGH heat, season with salt and pepper to taste.
Spoon the sauce over the lamb shanks. Recommend serving with a risotto milanese or polenta.