Gently rinse the mulberries in cold water, being careful not to crush them. Remove all stems as they can create an unpleasant texture in the finished jam. Pat berries dry with paper towels or let air dry in a colander.
Combine the clean mulberries with sugar in a large, non-reactive bowl (glass or stainless steel works best). Stir gently to coat all berries with sugar, then cover and let stand for 2-4 hours or overnight in the refrigerator.
While the berries macerate, sterilize your canning jars and lids by washing in hot, soapy water and placing in a 225°F oven for 10 minutes. Keep them warm until ready to use. Also, place a small plate in the freezer for testing the jam's consistency later.
Transfer the macerated berries and all juice to a large, wide pot. Add lemon juice, zest, and butter. Bring the mixture to a rolling boil over medium-high heat, stirring frequently to prevent sticking. If using pectin, add it now and stir to dissolve completely.
After about 20 minutes of simmering, test the jam's consistency by placing a small amount on your chilled plate. Wait 30 seconds, then run your finger through it. If it wrinkles slightly and doesn't flood back together immediately, it has reached the gel stage. If not, continue cooking and testing in 5-minute intervals.
Once the jam reaches the desired consistency, remove from heat. Stir in cinnamon and vanilla extract if using. Let stand for 5 minutes, then skim off any foam from the surface with a metal spoon.
Ladle the hot jam into warm jars, leaving ¼-inch headspace. Wipe the rims clean, place lids on jars, and screw bands until fingertip tight. Process in a boiling water bath for 10 minutes (adjust for altitude if necessary). Remove and let cool completely on a towel-lined counter.