Place cucumber slices, garlic, basil, oregano, water, rice vinegar, olive oil, cayenne pepper, salt, and black pepper into the bowl of a blender. Pulse 2 or 3 times. Blend on highest speed about 1 or 2 minutes until mixture liquefies. Strain through a fine strainer, pressing everything through with a spoon leaving just a few tablespoons of fiber and rough bits.
Cover and refrigerate until ice cold, 1 or 2 hours.
Ladle some gazpacho verde into chilled bowls. Scoop 1/4 cup burrata onto the soup. Drizzle with a few drops of olive oil.
