Place all ingredients in a heavy large pot; stir to combine. Bring to a rolling boil over medium-high heat. Boil, stirring occasionally, 15 minutes, adjusting heat as necessary to maintain an even boil.
While the mixture boils, mash fruit with a potato masher to desired consistency. Boil an additional 5 to 10 minutes, stirring frequently, or until slightly thickened (you'll see the bottom of the pot when stirring) and set.** (Temperature should be about 221 F.) Remove from heat; remove cinnamon stick.
Pour hot jam into 4 sterilized 8-oz. jars. Carefully wipe jar rims; cover. (Jam can be made up to 1 month ahead and refigerated or up to 6 months ahead and frozen.) To store at room temperature, immediately process in a boiling water bath for 5 five minutes.
Tips: * To peel peaches, drop peaches into larg pot of boiling water; boil 30 seconds or until peach skins loosen. Remove with slotted spoon; drop into ice water to cool. Use a knife to peel away skins.
** To test jam, before you begin cooking, place a small plate into the freezer to chill. When jam begins to thicken slightly, place a small amount of jam on chilled plate; return to freezer for 1 to 2 minutes (remove jam from heat during testing time). When set, jam will be slightly set and will not run on plate. If jam is too liquid, cook an addition 1 to 2 minutes before testing again.