Peel the pear, cut it in half lengthways and then remove the core with a spoon. Cut the pear into slices that are 3-5mm (⅛-¼") thick.
Mix the lemon juice with enough water to just cover the pear slices when placed in a bowl.
Peel the shallot, then dice it as finely as you can.
Strip the tarragon leaves from the stems, discard the stems, then finely chop the leaves.
Heat a 28cm or 11" frying pan (not non-stick) over a medium heat. Coat the pork chops in the oil, then season generously with salt, paying particular attention to the rind.
Cook the pork chops rind side down in the frying pan for around 10 minutes. The idea is to begin rendering down the fat and to crisp up the rind. I hold them together and then stand there and sear one half of the rind first, then rock them to sear the second half.
Once the rind has begun to crisp, turn the heat up to high and when the pan is hot, flip the chops down onto the flesh side and cook for 6 minutes.Flip the chops, cook for 1 more minute to sear the other flesh side a little, then transfer to a preheated baking tray in an oven at 220°C or 430°F and cook for a further 6-7 minutes.
Return the pan to a medium heat and add the butter. When it begins to foam, toss in the shallots and cook for 1-2 minutes, stirring continuously.
Pour in the cider and chicken stock, turn the heat up to high and reduce by two-thirds, this will take between 5-10 minutes. Ensure you scrape any crispy bits from the bottom of the pan and incorporate them into the sauce.
Whilst the sauce is reducing, heat a griddle pan over a high heat.
By now, the pork will have had its time in the oven. Check the temperature of the pork using a meat thermometer. I aim to remove the meat from the oven at 62°-65°C or 145°-150°F. Then rest the meat for 7-10 minutes. This will result in a perfectly cooked pork chop that has just a little pinkness when rested.
Once the sauce has been reduced, turn the heat down to a gentle simmer and then pour in the cream and add the tarragon. Gently heat until the pork is ready to serve.
Finally, dry the pear slices and cook them in a griddle pan for 1-2 minutes per side, then serve.