Arrange bread slices on a baking sheet. Bake for 6 minutes, until toasted.
Meanwhile, in a large stock pot, heat olive oil over medium heat. Add onion, celery, garlic, carrot, and broccoli. Pour broth over vegetables and increase the heat to high. Bring to a boil, reduce heat to medium and simmer 5 minutes. Using an immersion blender, puree until smooth or you can use a blender. Add milk and simmer 1 minute to heat through. Puree again. Season, to taste, with salt and pepper. Using a fork, mash garlic cloves with a pinch each of salt and black pepper, making a thick paste. Spread mixture on toasted bread and serve with soup.