Sprinkle pork with 1/2 tsp salt, then brown in oil in a large skillet over medium-high heat, turning as needed, 10 minutes.
Transfer pork and pan juices to a crock pot (5-6 qt size). Add the remaining 1 tsp salt, cider, brandy, 1 tbsp thyme, black pepper, and 1 sliced apple. Cover and cook until the meat is nice and tender, low and slow is best, 6-8 hours on low or 4 hours on high.
At about 20-30 minutes before the pork is done, heat 2 tbsp of butter in a large skillet over medium heat. Add the remaining 3 apples and cook, stirring frequently, until they are tender and have a light golden color to them, about 10 minutes. Transfer to a bowl and tent with foil.
When the roast is done, transfer it to a plate and tent it with foil to rest. Strain the juices and skim off the fat, set aside. Set aside the apple bits and pieces for later. Melt the remaining tablespoon of butter in the skillet, add the flour and cook, whisking often until golden and bubbly.
Slowly whisk in the juices and 1 tbsp of the thyme, cook until slightly thickened, 6-8 minutes. Transfer to a serving container. Slice the pork, place all the apples that you cooked on top of the pork, drizzle with gravy. Garnish with thyme sprigs and serve with more gravy for dipping.
