Place 16 of the blackberries in a food processor with the thyme
leaves. Pulse 30 seconds. Push the blackberry puree through a
fine-mesh sieve into a small bowl to remove seeds, pressing on
solids to extract as much liquid as possible.
Combine the blackberry puree, ice, tequila, syrup, lime, Cointreau,
and sparkling wine into a blender. Puree until smooth and well
combined. Divide between glasses, and garnish with additional
thyme and the reserved blackberries
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