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1
To make the ice cream, first pulse the sugar and basil in a food processor fitted with a steel blade until the mixture is a uniform green, and the basil is very finely chopped.
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2
Combine the basil sugar with the coconut milk, coconut cream, corn syrup, and salt in a medium saucepan. Cook over medium heat until the mixture simmers, stirring often.
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3
Using an immersion blender (or a regular blender), blend the mixture off the heat for 30 seconds (this helps emulsify the coconut oils).
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4
Carefully pour the mixture into a one gallon zip lock freezer bag, and submerge it in the ice water bath until cold, about 30 minutes.
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5
Freeze in the ice cream machine according to the manufacturer's instructions. Scrape into an airtight container, press parchment paper onto the surface of the ice cream, and freeze until solid, about 5 hours.
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6
To make the strawberry soda, combine the strawberries, sugar, balsamic vinegar, vanilla, and peppercorns in a medium saucepan and bring to a simmer over medium heat, stirring often.
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7
Reduce the heat to low, and simmer until the strawberries are very soft and have given up a lot of liquid, about 10 minutes.
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8
Strain through a fine mesh strainer, pressing gently on the strawberries to extract as much liquid as possible (you'll be left with a pretty wet mush--don't press too hard or you might get seeds in your syrup, depending on how fine your strainer is. Lining the strainer with cheese cloth will help keep the syrup seedless).
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9
Combine syrup with seltzer water to taste. This recipe made about three cups of syrup, which I combined with around 1.5 liters of seltzer water.
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10
Fill glasses most of the way with basil ice cream, and fill to the top with strawberry soda. Enjoy!
