Place the chopped pears, cinnamon stick, ginger, and vanilla bean into a large, wide-mouthed, heavy-bottomed pot. My creuset is perfect for this! Add the water and lemon juice, and bring to a boil.
Lower the heat to a simmer and cook until the pears are completely soft. The time for this will vary according to the hardness of the pears, but it took me about 30 minutes. Remove from heat.
Remove the cinnamon stick and vanilla bean, and set aside. Strain the solids out of the pear mixture into a large bowl using a food mill, chinoise, or other finely meshed strainer. Use a wooden spoon to push all of the pulp through the mesh if using a chinoise or other mesh strainer. Discard the solids (but not the cinnamon stick or vanilla bean).
Pour the pear purée into a large measuring cup designed for liquids - I recommend a 4-cup measuring cup - to determine how many cups of purée you have. This is very important in order to determine how much sugar to add.
Pour the purée back into the pot used for simmering the pears, and add 1/2 cup sugar for every cup of pear purée. Bring the pear mixture back to a simmer and stir with a large wooden spoon to dissolve the sugar. Add the reserved cinnamon stick and vanilla bean if you prefer a stronger cinnamon and vanilla flavor.
Maintain a simmer, stirring as needed to prevent the purée from sticking to the bottom of the pan. Initially, the stirring need only be occasional, but as the purée thickens into a butter/jam, the stirring will be very often. Towards the end, when the jam/butter is very thick, it will be necessary to stir it almost constantly to prevent caramelization of the sugar on the bottom of the pot. The entire process can take anywhere from 45 minutes to 2 hours, depending on many factors, but it took me just over 45 minutes.
There are a few ways to tell if the preserves have set up properly:
The setting temperature – the point where jams begin to gel – is generally 8˚F above boiling. Boiling at sea level is around 212˚F, so a jam’s setting temperature is around 220˚F. Boiling temperatures drop 1˚F for each 500 feet increased altitude above sea level. This is one of at least three ways to determine whether a jam has set up, but not necessarily the best or only method you should use.
Dip a large metal spoon into the hot, boiling jam. Ladle a little jam into the spoon, raise it above the pot, and pour the liquid back in. If the jam has set up properly, once most of the liquid has poured back into the pot, there will be at least two large drops formed that join together and drop into the pot in a sheet. This is called the sheet test, and sometimes the spoon test.
Chill a small plate in the freezer for at least 15 minutes. Ladle a little jam onto the chilled plate and return it to the freezer for 1 minute to cool. Remove and tilt the plate. If the jam runs easily, it’s not set up. If it moves very slowly – slower than molasses – it’s ready.
While the mixture is cooking, sterilize the jars for canning by carefully placing in a large pot of boiling water for 10 minutes along with the rings and lids. Dry up side down on a clean towel.
When the pear butter is ready, pour into hot, sterilized jars and seal, allowing for 1/4-inch head room between the pear butter and the tops of the jars. To ensure a good seal, I finish with a hot water bath for 10 minutes. A hot water bath means placing a rack on the bottom of pot of boiling water, and placing the jars of pear butter on the rack. They should be completely submerged in the water. Otherwise, I recommend storing the pear butter in the refrigerator.