1. To make the jam. Add the blackberries, honey, lemon juice, and lavender to a medium-size pot set over high heat. Bring the mixture to a boil. Once boiling use a potato masher or fork to break down and mash the berries. Continue to cook for 5-8 minutes or until the jam has reduced and thickened by 1/3. Remove from the heat and let cool. This should thicken more as it cools.
2. Line a 9×13 inch pan with parchment paper. In a bowl, combine the ice cream and jam until swirled/mixed. Don’t over mix, you want swirls. Spread the ice cream in an even layer, then cover and freeze until firm, at least 2 hours.
3. Preheat oven to 350° F. In a bowl, cream together the butter, honey, and vanilla until combined, 3-5 minutes. Add the flour, baking soda, cinnamon, and salt. Beat until combined. Mix in the white chocolate. Add 1 tablespoon of water at a time, until the dough comes together and forms a ball.
4. Divide the dough in half. Roll out one disk of dough between 2 floured pieces of wax paper to about 1/4 inch thickness. Cut 24 squares (roughly 2×2 inch). Transfer the cookies to a parchment-lined baking sheet. Repeat with the remaining disk of dough.
5. Combine the lavender and sugar, then lightly sprinkle the lavender sugar over the cookies. Bake 10-12 minutes. Let cool.
6. Remove the slab of ice cream from the freezer, cut into 12 squares. Sandwich the ice cream between the cookies. Freeze. Enjoy!
