Bring berries, sugar, and 1 cup water to a simmer in a covered medium sauce-pan over medium-high heat. Cook until berries are soft, about 10 minutes. Pass through a fine sieve into a bowl, pressing on solids to make a puree.
Bring 1/2 cup water, the garlic, ginger, vinegar, allspice, salt, and a generous amount of pepper to a simmer in a small saucepan over medium-high heat. Cook until reduced by half, about 5 minutes.
Pour vinegar mixture into a small bowl. Sprinkle gelatin on top; stir until dissolved. Stir mixture into berry puree.
Cover with plastic wrap; refrigerate at least 2 hours or up to 1 week.