Cook the pasta in a large saucepan of salted boiling water according to the pack instructions. Drain, then cool under cold running water and drain again. Tip into a bowl and toss through 1 teaspoon of the oil. Lightly beat 1 egg in a bowl and then mix together with the pasta.
Heat a large nonstick frying pan, add half the remaining oil and curl the pasta into small cakes about 3 cm (1 inch) wide. Add about 4 of the pasta cakes to the pan and cook for 2 minutes, flattening the cakes down with the back of a spoon. Turn the cakes over and cook for a further 1 minute until golden all over. Remove from the pan and keep warm. Repeat with the remaining pasta cakes to make about 12.
Crack the remaining 3 eggs into a small frying pan, dollop over the mascarpone and season well. Place over a low heat and cook for a couple of minutes until just beginning to set, then cook, gently stirring, for 3–5 minutes until creamy. Add the Parmesan and season well. Place 3 pasta cakes on each serving plate, spoon over a little scrambled egg and top with strips of smoked salmon. Serve sprinkled with chives.