Preheat oven to 400 degrees. Arrange tomatillos, onion and garlic on a pan. Drizzle with olive oil and roast for about 20 minutes, until vegetables are soft. Remove from oven and let cool completely.
In a blender, combine the cooled tomatillos, onion, garlic, ¼ cup of olive oil, cucumber, basil, lime juice, ½ teaspoon sea salt, honey, and yogurt. Blend until smooth. Taste and adjust seasoning. Chill the soup until ready to serve. Divide between bowls and garnish with torn basil leaves, sliced tomato and a drizzle of olive oil.