Combine blackberries, water, and sugar in a small saucepan.
Heat over medium until the berries soften and the sugar dissolves, about 3–4 minutes.
Remove from heat.
Transfer the mixture to a blender; blend until smooth.
Strain through a fine mesh sieve to remove seeds — this step matters for texture.
Stir in balsamic vinegar, lemon juice, black pepper, and a pinch of salt.
Taste: You want bright, fruity, and just a hint of warmth from the pepper.
Adjust lemon or pepper as needed.
Pour into a shallow dish or metal pan.
Freeze for 30–45 minutes, then scrape with a fork.
Repeat scraping every 20–30 minutes for 3–4 hours, until completely icy and fluffy.
Spoon into chilled bowls or coupes.
Optional finishing touches: A tiny crack of fresh pepper, A single micro-basil leaf, A drop of aged balsamic for shine