Preheat the oven to 400ºF and spray a baking sheet with non-stick cooking spray or drizzle with olive oil.
Next, add the broccoli, onion, garlic, and potato to the baking sheet.
Drizzle the vegetables with salt, pepper, and garlic powder and toss vegetables until they are coated in oil and spice.
Place the baking sheet in the oven and bake for 35-40 minutes (or until potatoes are soft), tossing the vegetables half way through.
While the vegetables are roasting, bring the chicken broth to a boil and then remove from heat and slowly whisk in the milk.
When the vegetables are soft remove them from the oven and remove 2 cups of vegetables from the pan and set them aside for later. These vegetables will be added to the soup right before serving for more of a chunky broccoli soup.
Next, carefully squeeze the garlic cloves from the head of garlic into the blender (being sure discard the paper from the head of garlic) the paper on the outside of the .
Add the rest of the vegetables to the blender along with the cheese and hot broth.
Blend on high until all ingredients are combined and the soup is smooth.
Finally, add in the last two cups of vegetables to the pureed soup, mix, and enjoy.