Preheat oven to 425°F. Place walnuts in a bowl and cover with hot water. Let stand while you prepare the rest of recipe.
Wrap garlic cloves in a piece of tin foil, and place it in the corner of a large baking sheet. Fill remaining baking sheet with cauliflower florets. Toss cauliflower in 1 Tbsp. olive oil (or avocado oil), 1/2 tsp. salt, and black pepper. Spread in a single layer and bake cauliflower and garlic for 35 minutes, tossing cauliflower once halfway through. Let cool at room temperature.
Once cool enough to handle, unfold tin foil and remove garlic cloves. Gently press garlic out of skins and transfer to a food processor (discard or compost skin). Drain walnuts and add to food processor, along with cauliflower, tahini, lemon juice, za'atar, sumac, remaining 1/2 tsp. salt, and 1/3 cup warm water. Blend mixture on high, gradually streaming in 1/3 cup olive oil, until mixture is mostly smooth, about 2 minutes. (You may need to stop once to scrape down the sides.)
Adjust seasonings as needed, and transfer dip to a serving bowl. Top with garnishes of choice (I like chopped chives, walnuts, olive oil, and sumac), and serve with crudités, pita, or dippers of choice.