THE OIL: Combine the paprika and oil in a liquid measuring cup, then strain through a coffee filter into a clean container. Set aside.
THE DIP: Heat the oven to 350°F. Put the sweet potato on a baking sheet, and season with salt and 1 tablespoon olive oil. Mix with your hands to coat. Roast until fully caramelized—about 25 minutes—and set aside. Meanwhile, heat a saute pan over medium-high heat and add 2 tablespoons olive oil. Add the onions, and cook until they are deep brown and fully caramelized, stirring occasionally. Set aside.
Using a standing or handheld mixer, whip chèvre until it’s light and fluffy, then slowly add ¼ cup smoked paprika oil, continuing to whip until the cheese mixture is airy. Fold in the onions, sweet potato, fish, and salt to taste. Serve.