Wash and zest the mandarins – I like using a Microplane to do this; it’s nice and sharp, and you can get the orange part off while leaving the white pith underneath. Set the zest aside and peel the oranges, tossing the white part and chopping the juicy flesh, working over a bowl or on a chopping board with a gutter to catch the juices. Pick out the seeds and put the chopped fruit into the bowl of a food processor and pulse until not quite smooth. (If you don't have a food processor, just chop it more.)
Combine the puree, zest, sugar and lemon juice in a large, heavy saucepan or small pot, and bring to a boil over medium-high heat. Reduce the heat and cook, stirring occasionally to make sure it’s not burning on the bottom, for about half an hour. Cut your vanilla bean in half lengthwise and scrape out the seeds with the tip of a knife; stir them into the jam toward the end of the cooking time. Test to see if it's jam by dropping a small spoonful on a chilled saucer – when you poke it with your finger, it should wrinkle.
Divide into jars or freezer containers and refrigerate for up to a month, or freeze for up to 4 months. Makes about 4 250 mL jars.