1. In a medium pot over high heat, bring sweetener and water to a boil. Add blueberries and return to a boil. Reduce heat to medium-low and simmer for 5 minutes, using a masher or wooden spoon to crush most blueberries as they cook to release juices. Turn off heat and stir in vanilla.
2. Strain into a heat-proof jar or pitcher, and transfer to refrigerator to cool completely.
3. Once cool, add 1⁄3 cup blueberry mixture and 1⁄2 cup sparkling water to each glass filled with ice. Top with cream if using and garnish with thyme and blueberries, as desired.