In a 1- to 1 1/2-quart pan over medium-high heat, stir blueberries, sugar, and 1/2 cup water until berries begin to pop, 4 to 5 minutes. Pour mixture through a fine strainer set over a bowl. Pour blueberries into a blender. Return berry syrup to pan.
Add lavender to syrup and stir over medium heat until syrup is infused with flavor, about 5 minutes. Strain into blender, pressing to extract liquid. Discard lavender.
Add cinnamon and vanilla to blender; whirl until mixture is smooth. Pour into a bowl, nest in ice water, and stir often until cold, about 15 minutes. Stir in half-and-half.
Pour chilled mixture into an ice cream maker (1 1/2-qt. or larger capacity). Freeze according to manufacturer's directions until firm enough to scoop. Serve, or transfer to a container and freeze, airtight, up to 1 week.
Note: Nutritional analysis is per 1/2-cup serving.