Bring boiling-water canner, half full with water, to simmer. Wash jars and screw bands in hot soapy water; rinse with warm water. Pour boiling water over flat lids in a saucepan off the heat. Let stand in hot water until ready to use. Drain well before filling.
Stem and crush strawberries thoroughly, one layer at a time (I use a potato masher for this). Measure exactly 4½ cups of prepared fruit and the balsamic vinegar into a large saucepan (at least 6-8 quarts).
Add the powdered pectin to the strawberries in the saucepan and stir to combine. Add butter (to reduce foaming).
Bring the mixture to a full rolling boil (a boil that doesn't stop bubbling when stirred) over high heat, stirring frequently.
Stir in sugar and return the mixture to a full rolling boil. Continue to boil for exactly one minute, stirring constantly. Remove from heat and skim off any foam with a metal spoon.
Add 1 tablespoon of the fresh ground black pepper and stir to combine. Take a little taste (careful, as it will be hot!) and add more pepper, if desired.
Ladle into the prepared jars, filling to within ¼ inch of the tops. Wipe jar rims and threads.
Cover the jars tightly with two-piece lids. Screw the bands on tightly. Place jars on elevated rack in canner. Lower rack into canner. (Water must cover jars by 1 to 2 inches. Add boiling water, if needed.)
Cover the pot and bring water to a gentle boil. Continue to boil for 10 minutes.
Remove jars and place them upright on a towel to cool completely. After the jars cool, check the seals by pressing the middle of the lids with a finger. (If lids spring back, lids are not sealed and refrigeration is necessary.)