Heat milk, sugar, and 1 tablespoon lavender honey over medium-high heat and bring to a boil. Stir until honey and sugar have dissolved, about 1 minute. Set aside to cool briefly.

Place goat cheese in a bowl and pour lukewarm milk mixture on top. Stir until smooth. Mix in cream. Refrigerate 8 hours to overnight.

Combine blueberries, water, and 1 tablespoon lavender honey in a saucepan over medium-low heat and slowly bring to a boil. Simmer for 15 minutes until most of the liquid has evaporated. Mash berries with a wooden spoon until mixture resembles chunky jam. Refrigerate 8 hours to overnight.

Pour goat cheese mixture into an ice cream maker and freeze according to manufacturer's instructions until it starts to thicken, about 10 minutes. Add blueberry mixture a little at a time; continue freezing, about 10 minutes more. Transfer to an airtight container and freeze until firm, about 4 hours.

Remove from freezer 20 minutes before serving.