Step 1 Season pork generously with salt. Set, skin side up, on a wire rack set inside a rimmed baking sheet. Chill at least 12 hours and up to 2 days.

Step 2 Preheat oven to 350°F. Pour 4 cups water into baking sheet with pork. Rub pork skin with oil; season with more salt. Roast, adding more water to pan as needed, until skin is golden brown and an instant-read thermometer inserted into thickest part of pork registers 195°F–200°F, 1 1/2–1 3/4 hours.

Step 3 Meanwhile, pour out 1/2 cup vinegar from bottle (save for another use). Remove pouring spout from bottle and add garlic, chiles, and a large pinch of salt. Cover and shake to distribute; let sit until ready to serve. (Or, combine in a glass jar or bowl).

Step 4 Bring hard cider and honey to a boil in a large saucepan; cook until thickened and very syrupy, 30–45 minutes.

Step 5 Increase oven temperature to 450°F. Continue to roast pork until skin is browned and puffed, 15–20 minutes (add a few more splashes of water to baking sheet if juices are scorching). Transfer rack with pork to a cutting board; let rest 20 minutes.

Step 6 Pour off fat from baking sheet and add 1/2 cup water, scraping up browned bits. Return baking sheet to oven for a few minutes if needed to help loosen browned bits. Stir into reduced cider mixture.

Step 7 Remove skin from pork, using the tip of a knife to get it started (it should come off in 1 large piece with a little help). Slice pork lengthwise into 2"-wide strips, then crosswise into 1/2"-thick pieces. Transfer to a platter and drizzle with reduced cider mixture. Break skin into large pieces and arrange on top; place a few chiles from vinegar around. Serve with chile vinegar.

Step 8 Chile vinegar can be made 1 week ahead. Store at room temperature.