Prepare soup: Heat olive oil in a large pot over medium high heat. Add broccoli, onions and garlic and cook, stirring occasionally, until vegetables begin to soften, 3-5 minutes. Stir in red pepper and nutmeg and cook an additional minute.
Add stock and bring to a boil. Reduce heat until soup simmers. Cover and simmer until broccoli is tender, 7-10 minutes.
Carefully ladle soup into blender and process until smooth. Return to pot and stir in cream or half and half.
Remove from heat and set aside.
Prepare mushrooms: Heat two teaspoons olive oil in a medium sauté pan over medium high heat. Add mushrooms and cook until mushrooms begin to brown, 5-7 minutes.
Ladle soup into four bowls. Spoon one quarter of the mushrooms onto each bowl of soup and serve.