Season the pork shoulder on all sides with the 1 tsp salt and 1/2 tsp black pepper.
Scatter the sliced onion and minced garlic in the bottom of the slow cooker. Place the seasoned pork on top.
Pour the apple cider and chicken broth around the pork. Cover and cook on low for 8 hours.
When the pork is done, lift it out and set it aside on a plate. Strain the cooking liquids into a saucepan, discarding the solids.
In a small bowl, whisk the flour with 3 tablespoons of the warm cooking liquid until smooth. Stir the mixture back into the saucepan and simmer over medium heat until the gravy thickens, about 5 minutes.
While the gravy simmers, place the potatoes in a large pot, cover with water, and bring to a boil. Cook until the potatoes are fork-tender, about 15 minutes. Drain well.
Return the potatoes to the pot. Add the butter, milk, and 1/2 tsp salt. Mash until smooth.
Shred or slice the pork and serve it with the mashed potatoes and apple cider gravy.