Generously salt and pepper the short ribs. Place a large pan over medium-high heat and add the olive oil. Once very hot, add the short ribs and brown on both sides, then remove from heat immediately.

Deglaze the pan with a little of the white wine, scraping the brown bits up as the wine reduces.

Add the meat, deglazing liquid, vegetables, and herbs to a 6 quart slow cooker and pour in the wine. Set temperature to low for 6 hours and let it cook.

While the meat cooks, start making the glaze. In a large sauce pan over medium-high heat, melt the butter to near foaming. Spread the brown sugar across the surface of the pan and nestle the garlic heads into the sugar. Allow to cook, and lightly caramelize for around 10-12 minutes.

Once the garlic and sugar are a nice dark brown, add the balsamic vinegar and turn up the heat, and allow to boil until reduced by 80%*. After the vinegar has reduced, add the chicken stock and reduce again, this time by 75%. Add the beef stock and reduce once more by about 75%, or until the glaze starts to thicken a bit, enough to coat a spoon with a light layer.

When the ribs are ready, remove from slow cooker and allow to cool. Reserve 1 cup of the braising liquid left in the slow cooker and add it to a large fry pan at medium-medium-high heat. Add 2 cups of the glaze, as well as 4 sprigs of rosemary, then add the ribs and allow the glaze to continue reducing around the ribs until thick and thoroughly glazed. Serve with pasta tossed in some of the remaining glaze and enjoy immediately.