In a large soup pot, heat olive oil over medium-high heat and sautégarlic and onions until translucent.
Add broccoli and cauliflower florets and about 2 tablespoons of the vegetable broth to generate steam.
Place lid on pot, reduce heat to medium, and steam vegetables for about 5 minutes.
Add curry powder and remaining broth.
Simmer until vegetables are very tender, about 15 minutes.
Once cooked, ladle broth and vegetables into a blender and purée until smooth.
Return to soup pot, heat over medium heat, and gradually whisk the yogurt and seasonings into the soup.
Once combined, do not bring to a boil to prevent the yogurt from curdling.
Serve warm.