Prep the peaches: peel (use a paring knife or blanch to loosen skins), remove pits, and roughly chop so you have about 5 1/2 cups. Stir the chopped fruit with the lemon juice to keep color bright and set aside.
Combine ingredients in a heavy-bottomed saucepan: add the peaches, sugar, cinnamon, and orange zest to the pot. Stir gently to distribute the sugar and spices evenly.
Bring to a simmer over medium heat, then reduce to low. Let the mixture bubble gently, uncovered, stirring and scraping the bottom every few minutes to prevent sticking. Continue simmering until the peaches are very soft and the volume has reduced — about 25–30 minutes.
Texture stage: remove the pan from the heat and mash the fruit with a potato masher for a chunkier butter, or use an immersion blender right in the pot for a smoother spread. If you prefer the silkiest finish, push the cooked peaches through a food mill into a clean saucepan.
Finish cooking: return the mashed or pureed peaches to low heat and simmer gently, uncovered, stirring frequently, until the mixture is thick enough to hold its shape on a spoon — about another 12–15 minutes. Stir in the vanilla once you remove the pot from heat.
Cool and store: let the peach butter cool to room temperature, then spoon into sterilized jars and seal. Refrigerate for up to two weeks. For longer storage, process in a water bath canner according to USDA guidelines.