Preheat oven to 400 degrees. Cut the tops off the garlic, drizzle with a little olive oil, and wrap each head individually in foil.
Place the cauliflower florets on a large baking sheet, and toss with olive oil, salt and pepper. Place the cauliflower and garlic in the oven. Bake for 30 mins, tossing the cauliflower halfway through. Cauliflower is done when it's soft and lightly browned. Pull the garlic from the oven at the same time as the cauliflower, and let it cool in the foil before handling.
Add the broth to a large stock pot, and heat on medium heat. Remove the garlic from the foil, and squeeze the cloves out of each head. Place in the pot with the broth.
Reserve 1/4 of the cauliflower on a cutting board, and place the rest of it in the pot with the broth and garlic. Bring to a boil, and once bubbling, turn the heat down and bring the soup to a simmer. Cook for 15 minutes.
Using a hand blender, (or a regular blender) puree the soup until smooth. Chop the remaining cauliflower into small pieces, and add to the soup after it's pureed. Add in the grated Asiago cheese, and stir until smooth.