Make the Peach Soup
Add the peaches, cucumber, honey, garlic, Greek yogurt, and kosher salt to a blender.
Blend until completely smooth and creamy.
Transfer the soup to the refrigerator and chill until very cold, at least 1 hour.
Spoon the chilled soup into serving bowls.
Drizzle with basil oil and garnish with cucumber slices, peach slices, or microgreens before serving.
Make the Basil Oil
Bring a small pot of water to a boil.
Blanch the basil leaves in boiling water for 45 seconds, then immediately transfer them to an ice water bath.
Squeeze excess water from the basil and place it in a blender with olive oil and salt.
Blend until smooth, about 1 minute.
Let the mixture rest for 30 minutes.
Strain the basil oil through a fine-mesh strainer and discard the solids.
Store the basil oil in a sealed jar in the refrigerator until ready to use.