Cook the cauliflower: In a large pot, bring the chicken broth to a boil. Add the cauliflower, lemon juice, and bay leaves. Cook over medium-high heat until the cauliflower is tender, about 10 to 15 minutes.
Prepare the cheese mixture: While the cauliflower cooks, mix the garlic, cream cheese, and Asiago cheese together in a bowl.
Combine and mash: Use a slotted spoon to remove the cauliflower from the broth and add it to the cheese mixture. Discard the bay leaves. Mash the cauliflower and cheese mixture with a potato masher until smooth. Season with salt and pepper to taste.
Finish the soup: Stir the mashed cauliflower mixture back into the broth. Mix well until smooth. Add the rosemary, thyme, and additional salt and pepper to taste.
Serve: Ladle the soup into bowls and enjoy the creamy, flavorful goodness!