Prepare the broccoli and cauliflower into small florets and set aside.
In a large pot or Dutch oven, heat the oil on medium heat and saute the broccoli and cauliflower for 3-5 minutes. Add the garlic and saute for an additional minute.
Pour in the chicken broth and heavy cream and bring to a boil. Immediately reduce the temperature and simmer for 10-12 minutes. Do not overcook the broccoli and cauliflower (you do not want it to be mushy).
Use an immersion blender to puree the mixture.
Keep the heat on LOW, and add the shredded cheddar cheese, stirring as you add it, until the cheese is melted.
Once the cheese is melted, salt and pepper to taste.
Serve right away. Optional to sprinkle the soup with a dash of Everything but The Bagel seasoning on top with a few more sprinkles of cheese and a sprinkle of green onion slices.