1. Place a few small plates in freezer. Combine apples and 2 1/2 cups water in a saucepan. Bring to a boil, reduce to a simmer, and cook, partially covered, mashing occasionally with a potato masher, until fruit is very soft, 10 to 15 minutes. Transfer fruit to a fine sieve set over a heatproof bowl; let drain without pressing on fruit, 4 hours. Strain again through sieve lined with damp cheesecloth. (You should have 2 cups.)

2. In a saucepan, bring juice, vinegar, salt, bell pepper, and hot pepper to a boil. Add sugar; return to a boil, stirring until sugar is dissolved. Cook, stirring, 11 minutes. Turn off heat. Place a small spoonful of jelly on a chilled plate; return to freezer 1 minute. Remove and push your finger through mixture; if it wrinkles, it is done. If not, return to a boil for 1 to 2 minutes, then check again. (Or cook until a thermometer registers 221 degrees.) Skim foam from top.

3. Ladle into clean containers, leaving 3/4 inch of headroom; let cool completely. Cover, label, and refrigerate up to 1 month, or freeze up to 1 year.