In a large blender or food processor, pulse the chopped pineapple until it is roughly shredded. You might need to do this in 2-3 batches. Be careful not to turn it into a smoothie!
Combine the pulsed pineapple and the rest of the ingredients in a small/medium saucepan and heat on low until all the sugar melts (start with 1.5 cups sugar, you can always add more later). Add cinnamon, if using (save the ginger for later if you want to add ginger).
Adjust flavor/consistency: Add more sugar and/or cinnamon if desired. Add more water if it is too thick, or simmer longer if it is too watery.
Allow to cool to room temperature, transfer to clean jars, cap, and enjoy!
Store this jam in the refrigerator for up to 3 months.