Heat the oven to 350ºF.
Add enough oil to a Dutch oven or high-sided skillet to coat the bottom. Heat over medium high. Season the pork with salt and pepper. Put the pork in the pan and brown on all sides; transfer to a plate. Pour off all but a few tablespoons of fat from the pan.
Reduce the heat to medium and add the onions and fennel to the pan. Cook, stirring occasionally, until the vegetables are tender and perhaps just starting to brown.
Stir in the vinegar, and let it simmer until it reduces by about half. Add the thyme, garlic, and red pepper, and simmer 1 minute more.
Return the pork to the pot, and add the chicken stock, apple cider, and canned tomatoes, plus enough water to barely cover the pork. Bring to a gentle simmer on the stovetop before transferring the pot to the oven.
Braise, uncovered, basting and turning the meat occasionally. Adjust the heat as necessary to maintain a gentle simmer (barely bubbling). The pork is done when it’s tender enough to cut with a fork, about 1-1/2 hours.
Transfer the pork to a plate, let the liquid cool, and spoon off any fat. (For a smooth, refined sauce, strain the liquid.) Bring the sauce–strained or not–to a simmer and reduce until it thickens enough to coat the back of a spoon. Return the pork to the pot.
Slice the pork and serve with the sauce, onions and fennel, and garnish with thyme leaves and whole slow-cooked garlic cloves, if using.