Preheat oven to 425 F.
Place the cauliflower and chickpeas in a large bowl. If you've just washed the cauliflower, pat it dry first to remove any excess moisture.
Whisk together the olive oil, lemon juice, salt, pepper, and oregano.
Pour the olive oil mixture over the cauliflower and chickpeas. Stir to thoroughtly coat the cauliflower.
Spread the mixture in a baking dish or sheet with sides so the cauliflower is only one layer deep. Use two pans if necessary.
Bake for 30-45 minutes, stirring every 15 minutes. You want the cauliflower to be tender but still have some resistance to a fork.
While the cauliflower roasts, blend or whisk together the tahini sauce ingredients. Use enough water to make the sauce pourable, but not too thin.
When the cauliflower is tender, plate the cauliflower and chickpeas in equal servings and pour the tahini sauce over the top. Sprinkle with fresh parsley.