Remove the stem from the cauliflower and chop into equal pieces. Toss with chickpeas, garlic, onion, salt and pepper, and about 5 tbs of olive oil. Spread evenly onto two cookie sheets sprayed with nonstick spray. Set aside.
Remove the stems from the broccoli and cut or pull the broccoli into equal bite sized pieces. Toss with remaining olive oil, salt, and pepper. Spread on a third prepared cookie tray.
Roast all trays of veggies in the oven for 20 minutes or until the broccoli and cauliflower are fork tender. Remove from oven. Set broccoli aside.
Add half of cauliflower, chickpeas, garlic, and onions to a blender with 16 ounces of veggie stock. Blend until smooth. Pour into a large soup or sauce pot and heat over medium low to medium heat. Repeat with the other half of the mix. Stir in cheese, carrots, roasted broccoli, and milk. Let heat until the the cheese is melted and soup is hot. Serve immediately, garnish with more cheese if desired.