In a large soup pot over medium high heat, add the olive oil to warm up for 1 minute, until glistening.
Add the minced garlic, chopped onions, carrots, and cauliflower to sauté for 5-6 minutes, until fragrant.
Stir in the oregano leaves, butter, and flour until well combined.
Add 2 cups bone broth to cool down the vegetables. Transfer to a high-speed blender to pulse until very smooth. Add back into the soup pot.
Whisk the remaining bone broth with the milk and yogurt (or heavy cream) in a separate bowl until smooth. Add into the soup pot and stir well.
Add the seasonings and broccoli florets. Stir to combine.
Bring to a boil, then reduce to a simmer. Stir in the grated cheddar and cook until broccoli is tender, about 10-15 minutes.