Place the chopped peaches in a large pot. Stir in the sugar, cinnamon, and lemon juice. Heat the mixture over medium heat for 30 minutes, stirring occasionally to make sure the mixture doesn't stick to the bottom of the pan. Remove from heat and stir in the vanilla extract.
Using an immersion blender, puree the peach mixture until desired consistency. I like to leave a few small chunks, but you can puree it until perfectly smooth if desired. If you don't have an immersion blender, you can use a blender or food processor. Let the peach butter cool to room temperature and transfer the peach butter to a blender or food processor and puree.
Let the peach butter cool completely. Pour into jars and store in the refrigerator. It will keep for about two weeks.
Note-this peach butter can be canned. Peach butter is great on toast, biscuits, pancakes, waffles, stirred into oatmeal, yogurt, or used as an ice cream topping!