Preheat the oven to 180°C/gas 4. Line a roasting tray with baking parchment and lay the sweet potato on it. Drizzle with 2 tablespoons of olive oil, sprinkle with salt and pepper, and roast until cooked through and lightly coloured, about 20 minutes.
While the sweet potato is cooking, heat a 24 cm sauté pan (a non-stick one is great when making a frittata) and caramelize the onion in 2 tablespoons of oil, adding the smoked paprika for the last few minutes of cooking.
Break the eggs into a bowl and add the olives, spring onion and a little salt. Once the sweet potato is cooked, add it to the eggs with the onion and mix well. Place the pan over a high heat and, when it’s fairly hot, add the remaining 2 tablespoons of olive oil, tilt to coat the pan base, then quickly tip in the egg mixture. Let it sit undisturbed for 30 seconds, then slowly mix it, taking the raw inner part to the outside and bringing the cooked outside into the centre. Cook it like this for 2 minutes, making sure it doesn’t catch on the bottom. You can now either place the sauté pan (if it’s ovenproof) in the oven and cook for 8–10 minutes, or place it under a hot grill for 6–8 minutes until it’s cooked through. The frittata should be almost firm to the touch, with just a little give. Take it away from the heat and leave it to rest in the pan for 10 minutes before carefully inverting it on to a large serving plate. Leave to cool down.
A frittata is almost better after 4–5 hours than it is straight from the pan, so it’s a good idea to make it ahead of time. It will keep out of the fridge in a cool place for up to a day; just make sure it’s tightly covered, away from the sun and heat.