Preheat oven to 350°.
Place the butternut squash pieces, cauliflower florets and garlic cloves in a pile in mixing bowl. Drizzle 2 tablespoons of extra virgin olive oil over the vegetables, and sprinkle the smoked paprika, cumin and salt. Toss well to combine then spread onto a single layer on the baking pan on parchment paper.
Roast the vegetables in the preheated oven until tender, about 12-14 minutes. Remove from the oven and cool slightly.
Scrape the vegetables and any remaining oil into a blender or food processor. Add the drained chickpeas, tahini, lemon juice and 1/4 cup olive oil to the vegetables in the blender. Purée until smooth. If the mixture is having trouble blending, add water 1 tablespoon at a time until smooth. Once blended taste and season with more salt if needed.
To serve, spoon into bowls, and top with a swirl of fresh olive oil and a sprinkle of smoked paprika.