To make black pepper simple syrup, combine 1 cup of water, 1 cup of sugar and 5 tablespoons of crushed black peppercorns. Bring to a simmer in a small pot, remove from heat, strain and refrigerate until cold.
Combine black pepper simple syrup, blackberries, and basil in a glass and muddle well. Fill a tall glass with ice.
Fill glass with two parts fresh squeezed lemon juice to one part club soda, and mix well.