Preheat oven to 325 degrees.
Pat ribs dry with paper towels and season with salt and pepper on all sides.  Heat 2 tablespoons of butter in a large dutch oven over medium-high heat. Add the ribs and brown on all sides.  Transfer the ribs to a plate, then add the garlic and stir until softened but not brown, about 1 minute.  Carefully pour in the wine, bring to a boil and cook until reduced to about 1 cup.  Add the ribs and any juices they have released back to the pot along with the stock.  Reduce and heat and bring to a simmer, then cover the pot and transfer it to the oven, to braise, until the meat easily falls off the bone. About 3 hours.
Transfer the ribs to a plate and tent with foil to keep warm.

Strain the braising liquid through a fine mesh sieve into a saucepan set over medium-high heat.  Simmer the liquid, skimming fat as necessary, until thickened, about 10 minutes.  Remove from the heat and whisk in the remaining 1 tablespoon of butter.  Taste for seasoning and adjust if necessary.
Transfer the ribs and sauce to a serving dish and enjoy.