Make the Soup: In a blender, puree the cucumbers, avocado, parsley, mint, lime juice and Greek yogurt until smooth. Season with salt and pepper.
Make the Garnishes: Preheat the oven to 425°F. Place the baguette, cut sides up, on a parchment-lined baking sheet. Butter the baguette and top with the Asiago cheese. Bake until the cheese is fully melted and golden brown, 10 to 12 minutes.
Meanwhile, in a small bowl, whisk together the Greek yogurt and lime juice.
Serve the soup topped with the lime yogurt and with the warm, cheesy baguette on the side.
