Cut the pears into 1-inch chunks. Cut the apples in half or into quarters if large. Put the fruit and the cider in a very large pot (at least 7-quart capacity). Bring to a boil over high heat. Reduce the heat to medium low and simmer, stirring frequently, until the fruit is very soft when pierced with a knife, 40 to 60 minutes. Take the pot off the heat.
Set a food mill fitted with a fine sieve disk over a large bowl. Purée the fruit in small batches, discarding seeds and skins.
Wipe out any remaining seeds or peels from the pot and pour in the purée. Add the maple syrup, brown sugar, cinnamon, cloves, and salt. Stir until well blended.
Bring to a boil over high heat. Reduce the heat to low or medium low to maintain a simmer. Using a large spoon, skim off most of the foam that rises to the surface during the initial simmering.
Continue simmering, stirring often with an angled spatula, making sure to scrape the bottom, corners, and sides of the pot, until the purée becomes thick and dark and the bubbling becomes slow and laborious (more like volcanic burps than bubbles), 1-3/4 hours to 2-3/4 hours. Be sure to stir toward the end of cooking to avoid scorching. To test for doneness, spoon a dollop of the butter onto a small plate and refrigerate for a minute or two. It should hold its shape with no water separating out around its edge.
Remove the pot from the heat and add the lemon juice and vanilla, stirring until well blended. Transfer the butter to a container, let cool to room temperature, and then store, covered, in the refrigerator for up to 3 weeks.
Note: For longer storage at room temperature, can the fruit butter. Transfer the hot butter to clean, hot canning jars, leaving 1/4 inch of headspace in each jar, and follow the directions in our canning video, processing the butter for 10 minutes.