Frying the sausage: Heat 1 tablespoon of the oil in a large deep skillet or shallow braising pan (12-inch) over medium heat. Add the sausage and fry, stirring often, until browned on most sides, 6 to 8 minutes. With a slotted spoon, transfer the sausage to a paper towel-lined plate to drain.
The aromatics and braising liquid: Pour off and discard the fat from the pan. Add the remaining tablespoon of oil and heat over medium heat. Add the onion, season with salt and pepper and saute, stirring, until the onion begins to soften and brown on the edges, 4 to 5 minutes. Add the garlic, stir and saute for another minute, until fragrant. Add the white wine, stir and scrape the bottom of the pan with a wooden spoon, and boil until the wine is reduced by about half, about 4 minutes. Add the vinegar, stir, and boil for a minute or two. Add the stock and bring to a simmer.
The braise: Season the pork all over with salt and pepper. Add the chops to the skillet, and immediately reduce the heat to a gentle simmer. One by one, tear the peppers into small pieces, discard the seeds and stems, and adding the pieces to the skillet. (I like to hold them over the skillet while I tear them so that the juices fall directly into the pan. The only trouble with this approach is that a few errant seeds will fall in too, making the dish spicier still. If you'd prefer to minimize the peppers' heat, tear them over a cutting board so that any juices drip onto the board, then scrape every last seed to the side, and add the peppers and as much of the juices as you like to the skillet.) Cover the skillet and braise the pork quietly, checking after 5 minutes to see that the liquid is not simmering too furiously. If it is, lower the heat or set a heat diffuser beneath the pan. After 20 minutes, turn the pork with tongs. Continue to braise at a gentle simmer until the pork is fork-tender, about 40 minutes total.
The finish: Transfer the chops to a platter or plates and cover loosely with foil to keep warm. Bring the cooking juices to a boil over medium-high heat. Skim any surface fat with a large spoon. Boil until the juices are tasty and slightly thickened, 8 to 10 minutes. Lower the heat to a simmer, add the sausage to the sauce, and simmer for about 3 minutes to heat through. Taste for salt and pepper. Spoon over the pork and serve.