Put the plums, sugar, vanilla beans, and cinnamon in a large wide saucepan. Squeeze the lemon juice through a strainer into the pan. Cook over medium-high heat, stirring occasionally, until the sugar dissolves and the mixture boils, about ten minutes.
Reduce the heat to medium and continue to cook, stirring occasionally, until a candy or deep-fry thermometer registers 220F, about 30 minutes. To be sure that the mixture has reached the gel point, spoon some onto a chilled plate and put in the freezer until cool. The liquid should set; if not, continue to cook and retest after a few more minutes. Remove the pan from the heat and let cool 30 minutes.
Meanwhile, if canning, sterilize four 8-ounce canning jars and lids
Return the plum mixture to medium-high heat. Bring to a boil, stirring, then add the plumcots. Reduce the heat to medium and simmer until the plumcots are tender, about 5 minutes. Discard the cinnamon sticks and vanilla pod pieces if still present.
Fill the jars with the plum mixture, leaving 1/2 inch headspace, then seal and process.