Heat olive oil in a large pot over medium-high heat. Add onion and garlic and saute until the onions begin to turn translucent; lower heat if browning starts to occur. Add spices and saute a minute or so. Add tomatoes, chickpeas, broth, and sugar. Season with a couple pinches of salt and 10 grinds fresh pepper. Stir well. Chickpeas should be just covered with liquid. If level is shy, add some water so the chickpeas are just covered.
Bring to a simmer, then lower heat to low and gently simmer for 45 minutes.
Remove soup from heat. Use a potato masher to mash up some of the chickpeas right in the pot. Stir in the spinach and let heat through until wilted, just a couple minutes.
Season again, to taste, with salt and pepper.
Serve soup, drizzled lightly with extra-virgin olive oil, if desired.