Add the blackberries to a large pitcher and lightly mash them just enough to release juice and aroma while keeping some structure, then add the honey and stir until fully dissolved; pour in the fresh lime juice and mix gently to combine without crushing seeds.
Pour in the ice-cold water to reach a total volume of about 3.2 liters, add the whole blackberries and thin lime slices, and stir gently to distribute without breaking down the fruit.
Refrigerate for at least 1 hour for a clean, light flavor; for a deeper berry profile, infuse up to 4 hours, but stop there — extended contact dulls blackberry brightness and muddies the finish.
Serve well chilled, straight from the pitcher or over ice if preferred.
