Preheat the oven to 350 degrees F (175 degrees C).
Cut off the top 1/4-inch of the garlic cloves and brush the cut cloves with a small amount of olive oil. Wrap in aluminum foil.
Bake in the preheated oven until cloves are tender and browned, about 45 minutes. Let cool until safe to handle, about 5 minutes; chop.
Heat olive oil in a 5-quart pot over medium-high heat. Add garlic and onion; saute until onion is translucent, about 5 minutes. Add butternut squash and broth. Season with salt and pepper. Bring to a boil, reduce heat, and simmer until squash is soft, about 30 minutes. Remove soup from heat and let cool slightly, about 30 minutes.
Fill blender halfway with soup. Add about 1/2 cup of almond milk. Cover and hold lid down with a potholder; pulse a few times before leaving on to blend for 1 minute. Pour into a pot. Repeat with remaining soup and almond milk. Return soup to the stove over low heat before serving; cook until heated through, about 3 minutes.