Heat 3 cups water in a saucepan over high heat until steaming; reduce the heat to low and cover to keep hot. Heat 1 tablespoon olive oil in a paella pan or very large skillet over medium-high heat. Add the cauliflower and season with salt and pepper. Cook, stirring occasionally, until browned in spots, about 2 minutes. Transfer to a bowl.
Add 2 more tablespoons olive oil to the skillet. Add the mushrooms in an even layer and season with salt and pepper. Increase the heat to high and cook, stirring, until browned and tender, 4 to 5 minutes.
Add the remaining 1 tablespoon olive oil, the scallion whites, garlic and paprika; stir until the paprika is toasted, 30 seconds. Stir in the wine and cook until the pan is almost dry, about 1 minute. Add 3 cups hot water, the cauliflower, rice, 1 teaspoon salt and a few grinds of pepper. Stir once to distribute the ingredients but don?t stir again. Bring to a boil, then reduce the heat to medium low; cover with a lid or foil and cook until the liquid is absorbed and the rice is tender, about 14 minutes.
Uncover and arrange the roasted pepper and olives on top. Increase the heat to medium to crisp the bottom, moving the pan for even browning, about 1 more minute. Top with the parsley and scallion greens.