When frozen as directed, the yogurt will have a light granita texture that can be easily scraped with a fork. If you prefer a smoother texture, you can spin the yogurt mixture in an ice cream maker according to the manufacturer's instructions.
Combine 1/4 cup of the blueberries, 2 tablespoons water, 1 tablespoon honey and the thyme sprigs in a small heavy saucepan. Coarsely mash the blueberries using a fork or a potato masher. Place over medium-high heat and bring to a boil. Remove the pan from the heat, cover and let the mixture stand for 15 minutes. Uncover the pan and let the syrup cool slightly. Discard the thyme sprigs.
Place the remaining blueberries, remaining 1/3 cup honey, yogurt, agave, lemon juice and cooled blueberry syrup in a blender or food processor. Blend until the mixture is almost smooth.
Transfer the yogurt mixture to a shallow glass baking dish, cover and freeze until slushy, about 2 hours. Using a fork, stir to blend. Continue to freeze until firm, at least 8 hours or overnight. Using the tines of a fork, scrape the mixture into small serving bowls or glasses. Serve immediately.
This recipe has been updated and may differ from what was originally published or broadcast.