Begin by adding 1 cup of blackberries to a large heavy pot. Crush with a potato masher and repeat the process until all 10 cups are used up.
Stir in pectin and sugar, and bring to a full boil over medium heat, stirring often.
While it's cooking, prepare the jars by filling each one with boiling water (I put mine in a large pot in a clean sink). Place the lids and screw bands in a saucepan, cover with water, and simmer over low heat on the stove.
Add honey and lemon juice, and return to a full boil, stirring constantly.
Turn heat off and stir in rosemary.
Just before filling each jar, dump the water out, dry outside with a clean cloth and laddle the hot jam mixture in until it's ¼" from the top (be careful not to burn yourself!). Wipe the jar rim with a clean towel and place a lid from the saucepan over top. Screw a band on until just tight. Quickly repeat the process until all of the jam is used up.
Place jars in a boiling water bath (water should cover top of lids) for 10 to 15 minutes, remove and rest on the counter undisturbed until cooled. See notes below for sealing instructions.