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Cook the spaghetti. Meanwhile, melt the butter in a small pan, add the garlic and gently sizzle for 1 min. Remove from the heat.
Lightly beat the cream, eggs, softened garlic and half the Parmesan in a bowl. Stir in the smoked salmon trimmings.
Drain the pasta well and return to the pan. Add the salmon mixture and the chives, then toss well so the heat from the pasta lightly thickens the sauce. Serve scattered with the remaining Parmesan and plenty of black pepper.