Preheat oven to 350 degrees F. Line a pan with parchment paper. Place the rinsed chickpeas on the pan and pat dry. Drizzle with olive oil and sprinkle with the curry powder, Garam Masala, and spices.
Bake at 350 degrees F for about 45 minutes, shaking the pan now and then to redistribute the chickpeas. Remove from oven to cool.
Make the soup:
Saute the onion and garlic in olive oil in a large pot over medium heat for about five minutes.
Add the potatoes and broth and raise heat to high. Bring to a boil, then reduce to a simmer and simmer for about 15 minutes until potatoes are tender.
Add broccoli florets and raise heat to medium. Cook until broccoli is tender and bright green, about 10 minutes.