If not already chopped, cut the pork into large bite-sized pieces, trimming and removing excess fat and sinew off the pork as you go. Cut the bacon in thin slices. Dice the onion and peel and cut the carrots into large bite-sized pieces.
Preheat the oven to 340F/170C.
Warm the oil in a heavy based Dutch oven or similar pan/pot over a medium-high heat. Sear the pork on all sides in batches so that you don't overcrowd the pan, cooking a couple minutes each side to let it brown. Remove once browned and repeat with the next batch until all of the pork is browned.
Add a little more oil, if needed, and onion, cook a minute then add bacon to the pan. Cook for a couple minutes until the onion softens and bacon is cooked but not yet crisp. Add the carrots to the pan, stir through and cook a minute or two then add the flour to help absorb the fat (it will also help the sauce thicken).
Pour over the cider to deglaze and and stir to mix in any browning from the pan. Add the stock, season with pepper and add the tarragon. Add back the pork. Mix everything and bring to a simmer then cover and place in the oven.
Cook in the oven for approximately 2 hours until the pork is tender. As the pork is nearing being done - around 15- 20 minutes before - cut the apples into slices and remove the core - if you cut the apples in quarters, remove the core at this point then slice the quarter into around 4 slices, depending how large the apple is.
Warm the butter in a large skillet/frying pan over a medium heat and once bubbling, add the apple slices in a single layer. Cook for a few minutes on both sides until gently brown and the apples are soft.
Once the pork is tender, remove the pot from the oven and add the cream. Mix it through well. If you prefer the sauce to be a little thicker, you can add a little more flour or corn starch (cornflour) mixed with water to form a paste and mix in well. Add the apple slices, mix through and serve.