Divide oranges, and peel one half, discarding the peel. Separate the orange slices and dice them into chunks, keeping as much juice as you can. Deseed if necessary.
Take the unpeeled oranges, and cut off their ends. Chunk them up keeping as much juice as you can. (Bigger chunks yield candied fruit-like jam, while smaller chunks result in a smoother jam.) Deseed if necessary.
In a deep pot, add all the orange pieces, the juice, ½ cup of water, and lemon juice. Turn the temperature down to the lowest setting. Cook for 40 minutes stirring every few minutes.
Add sugar and vanilla to the oranges, stir thoroughly, and cook for another 10-15 minutes. (If the oranges were particularly juicy you may need to cook 10-15 minutes longer.)Turn the heat off.
Using a stick (hand) blender, blend the orange jam down to desired consistency.