Cook the pasta in a large saucepan of salted boiling water according to the packet instructions until al dente.
Meanwhile, melt the butter in a large frying pan over a medium heat. When the butter starts to foam, add the Parma ham and cook, stirring, for 2–3 minutes. Season the red mullet with salt and pepper and add to the pan, skin-side down. Scatter with the sage and cook for 2–3 minutes until the fish is opaque all the way through. If the butter begins to colour too much, reduce the heat slightly.
Drain the pasta, reserving a ladleful of the cooking water, and toss into the frying pan with the fish. Stir gently to combine, then add the reserved pasta cooking water and stir over a medium heat until the pasta is well coated and looks silky. Serve immediately.