First, prepare honey ginger simple syrup by combining honey, water, and minced ginger into a small sauce pan. Bring contents to a boil, stirring often. Then, reduce to low and let simmer for 10 minutes. Strain and then place in refrigerator to cool.
Next, place a 6 oz. carton of Driscoll's Raspberries, 1/4 cup of lime juice, and 2 teaspoons of fresh ginger into a food processor or high speed blender. Blend until pureed.
Use a sieve and spatula to remove seeds and any other chunks from the puree.
Slap 3 mint leaves to release flavor and place in a cocktail shaker. Then add 2 tablespoons of raspberry puree, 1.5 oz. honey ginger simple syrup, 1.5 oz. white rum, and a handful of ice. Gently shake until combined.
Pour over a cup of ice and then add 1.5 oz. of club soda. Repeat 3 more times.
Serve with a lime wedge and fresh raspberries.