Preheat the broiler. (If possible, position the broiler rack 3 inches from the heat.) Mix the breadcrumbs, 1 tablespoon olive oil, the parsley and a pinch of salt in a small bowl. Soak the saffron in a separate small bowl with 1 tablespoon water.
Heat 1 tablespoon olive oil in a large nonstick ovenproof skillet (preferably cast iron) over medium-high heat. Add the scallops, season with salt and sear until golden, about 2 minutes. Flip and cook 1 more minute; transfer to a plate (do not wipe out the skillet).
Heat the remaining 1 tablespoon olive oil in the skillet. Add the onion and carrots, season with salt and cook until the onion is soft, about 4 minutes. Add the garlic and paprika and stir until toasted, about 1 minute. Add the wine, scrape up any browned bits and cook until the liquid is almost evaporated, about 1 minute. Stir in 1 1/2 cups water, the saffron and soaking water, and any juices from the plate of scallops. Bring to a simmer and cook until about 1/4 inch of liquid remains, 8 to 10 minutes. Season with salt.
Remove the skillet from the heat and stir in the butter until melted. Return the scallops to the skillet, transfer to the broiler and cook, rotating the skillet as needed, until the scallops are firm, 1 to 2 minutes. Sprinkle the scallops with the breadcrumb mixture and continue to broil until browned, 1 to 2 more minutes, rotating as needed.