Heat the oven to 425ºF.

• Cut the cauliflower into 1-inch florets, discarding any leaves or thick stalks.

In a medium bowl, combine the cauliflower, paprika, and 2 teaspoons oil. Season with salt and pepper and toss to coat.

• Pat the chicken dry with a paper towel; season generously with salt and pepper.

In a large frying pan over medium-high heat, warm 1 tablespoon oil until hot but not smoking. Add the chicken, skin side down, and cook until the skin is golden brown but the meat is not yet cooked through, 4 to 5 minutes. Turn the chicken and cook for 30 seconds. Transfer the chicken, skin side up, to one end of a sheet pan (do not clean the frying pan). Spread the cauliflower in an even layer on the other end of the sheet pan (do not clean the bowl). Roast until the chicken is cooked through, 10 to 12 minutes; transfer to a plate to rest. Continue roasting the cauliflower until browned and tender, 6 to 8 minutes longer. Return the cauliflower to the bowl to cool slightly.
While the chicken and cauliflower roast, prepare the scallions.

• Trim the root ends from the scallions; cut the scallions into 1-inch lengths.

In the same pan used for the chicken, add the scallions and cook over medium-high heat, stirring once or twice, until charred, 3 to 4 minutes. Transfer to a plate.

• Strip the parsley leaves from the stems; coarsely chop the leaves.

Add the scallions, parsley, and olives to the roasted cauliflower and stir to combine. Season to taste with salt and pepper.

Divide half the green romesco between individual plates and top with the chicken. Serve with the cauliflower and the remaining romesco on the side.