Preheat oven to 450 degrees Fahrenheit.

In a large bowl, toss cauliflower florets with one and a half tablespoons olive oil, paprika, half a teaspoon salt, cumin, crushed red pepper, and garlic. Mix well.

Spread florets evenly on a large rimmed baking sheet. Roast until lightly browned and a little crispy, about 18 to 20 minutes. Let cool.

Combine roasted cauliflower along with any juices, tahini, remaining three tablespoons olive oil, lemon juice, and remaining one and a half teaspoons salt in a food processor. Add half a cup water and blend, adding more water if needed (up to 1/4 cup) and scraping sides often, until mixture becomes a creamy purée, about four minutes. Add parsley and mint and pulse just to blend. Taste and add more salt or lemon juice, if needed.

Spoon into a serving bowl and sprinkle with a pinch of smoked paprika.