Place oven rack in middle position. Preheat the oven to 500°F.
Mix 2 tablespoons oil, 2 teaspoons cumin, cauliflower, and a pinch of salt and pepper in a large bowl. Toss well, then pour onto one-half of a baking sheet.
Rub the remaining oil onto the chicken legs. Season with the rest of the cumin, and a pinch of salt and pepper. Place on the open end of the baking sheet, skin side up.
Place baking sheet in the oven and cook for 10 minutes. Flip the cauliflower and the chicken legs, and return sheet to the oven. Cook for 10 more minutes. Flip again, then cook for a final 5 to 10 minutes. Remove when both the cauliflower and the chicken are nicely browned.
Meanwhile, mix together the tahini, garlic, lemon juice, and 1/2 cup of water in a bowl. Season with salt.
Serve the chicken and cauliflower with the tahini sauce. Dust with a pinch of smoked paprika.