Start by thoroughly washing and drying your lemons. Cut them in half and squeeze out the juice, making sure to catch any seeds, and reserve it aside.
Slice the squeezed lemon halves into very thin slices, and don't disregard any bits – everything goes in there it will give the jam a beautiful intensity and depth.
Place the lemon slices, lemon juice, sugar, and water in your pot and stir to combine.
Bring the mixture to a boil over medium heat, stirring frequently.
Once boiling, reduce the heat to medium-low and simmer, stirring often, until the jam thickens this will take approximately 1 hour. The jam should thicken and coat the back of a spoon. If you have a candy thermometer, the temperature should reach 220°F (104°C), also known as the "thread stage."
Remove the saucepan from the heat and let it cool for a few minutes. If using, stir in the vanilla extract.
While the jam is hot, carefully ladle it into your sterilized mason jars, leaving about 1/4 inch of space at the top, and seal immediately.