Combine peaches, cucumber, onion, garlic, bell pepper, and tomatoes in a blender. Season with salt, cumin, and cayenne. Pour in vinegar, lime juice, olive oil, and water. Blend until smooth, starting with a few pulses and finishing on high speed.

Strain soup through a fine-mesh strainer into a large bowl. Cover with plastic wrap and refrigerate until completely chilled, at least 3 to 4 hours.

Stir soup and season to taste. Pour into serving cups and garnish with feta, diced peach, basil, and a sprinkle of cayenne.