Mash blackberries in mixing bowl until they become very juicy, then pour juice, pulp, and seeds into quart-sized Mason jar. Add vinegar, peppercorns, and thyme. Screw lid on tight and shake jar for several minutes to ensure fruit and vinegar are mixed well. Set jar in dark space, such as inside a cupboard or covered with a towel on countertop. Shake mixture a few times daily for 1 week to macerate fruit. After 1 week, strain herbs, spices, and pulp from juice and discard. Clean Mason jar and pour liquid back into it. Add sugar. Screw lid back on and shake vigorously to incorporate sugar into liquid. Once again, leave jar in dark place, and shake it 3 times daily for 1 week. Store shrub in refrigerator to prevent further fermentation. Shrub will keep at least 2 weeks.