Heat olive oil in a large soup pot, add the onion and 1 teaspoon salt and pepper and sauté for 5 minutes. Stir in the garlic and cook 1 more minute.
Set aside cauliflower florets from one half of one of the cauliflower heads. Add the remaining cauliflower florets, even stems (you can use everything but the hard core), and potatoes and sauté for 5 more minutes.
Add chicken stock and bring to a boil, then simmer for 30 minutes.
While the soup is cooking, rinse the broccoli and trim florets into "small-medium" bite-sized pieces. Place vegetable steamer basket in a second pot with 1 inch of water, and bring the water to a boil. Then add broccoli florets, and the cauliflower florets previously set aside. Steam for 6-7 minutes, just until the broccoli is al-dente. Remove from heat, rough chop and set aside.
After soup mixture has simmered, remove from the heat and stir in Worcestershire sauce, dry mustard, Sriracha, paprika, and almond milk. Using an immersion blender, carefully puree the soup until smooth. (You can also blend this in a food processor in batches.) Stir in the cheddar cheese until melted and creamy. ***NOTE: Use less Sriracha if you want less kick in this soup!**
Reserve 1 1/2 cups of the steamed broccoli and cauliflower for garnish and stir the rest into the warm soup.
Serve warm, garnishing with the steamed broccoli & cauliflower florets as well as more shredded cheddar cheese if desired.