Blackberries give this vodka cocktail its gorgeous hue and jammy flavor. Use the leftover simple syrup to mix up drinks for friends or skip the vodka for a mocktail.
Set a fine-mesh strainer over a heatproof bowl. Muddle blackberries, rosemary and sugar in a small saucepan until almost smooth. Add water and bring to a simmer over medium-high heat. Cook, stirring occasionally, until fragrant and deep purple, about 5 minutes. Strain the mixture into the bowl, pressing on the solids to extract as much juice as possible. Refrigerate until cool, about 30 minutes.
Combine 1 ounce of the syrup, vodka and lime juice in a glass. Add ice and top with seltzer. Garnish with more rosemary and a lime slice, if desired.
To make ahead: Refrigerate syrup (Step 1) for up to 1 week.
1 alcohol equivalent, 1/2 other carbohydrate