In a small saucepan, melt the sugar in 1/2 cup water over medium heat to make a simple syrup. Let cool.
Place 8 thyme sprigs in the bottom of a cocktail shaker. Pour in the simple syrup and, using a muddler or wooden spoon, lightly crush the thyme. Stir in the lemon juice.
Strain the mixture into a small pitcher. Stir in the vodka and refrigerate until chilled, about 1 hour.
To serve, fill 8 rocks glasses with ice. Pour in the vodka mixture and top off each drink with some of the cava. Garnish with the remaining thyme sprigs.