Blackberry Lemon Variegate: Combine 1/2 oz. granulated sugar, pectin and water in small bowl. Stir until sugar is dissolved.
Add remaining ingredients to medium saucepan; whisk until blended. Whisk in pectin mixture and remaining sugar. Bring to boil on medium heat, stirring frequently. Boil 1 min. Transfer to clean bowl and chill over an ice bath. Refrigerate until ready to use. (Note: Not all of the Variegate is used for this recipe. Keep leftovers refrigerated and use for future batches of ice cream.)
Ice Cream: Combine milk and cream in medium saucepan. Whisk in combined sugar, dextrose, dry milk and ice cream stabilizer. Cook on medium heat, stirring occasionally, until mixture reaches 165°F. Remove from heat; strain.
Pour small amounts of mixture into blender and process 30 seconds. Transfer to clean bowl and chill over an ice bath. Continue until all of mixture has been processed. Stir in vanilla. Refrigerate overnight.
Freeze mixture in ice cream maker according to manufacturer's directions. Gently stir in cookie pieces. Layer ice cream and Blackberry Lemon Variegate in freezer container. Swirl with a spatula to create rippled effect. Freeze until firm.
For each serving, use #16 scoop to portion 2 scoops (6.5 oz.) ice cream into serving dish.