Wash the rice in cold running water.
Warm the butter and olive oil in a large shallow pan with a lid. Add the orzo and cook for 1 minute, until it starts to turn golden-brown. Add the washed rice and cook for 2 minutes, stirring constantly.
Pour over the chicken stock, bring to the boil and then simmer for 10–15 minutes, or until softened but still with a little bite.
Discard any mussels with broken shells and any that refuse to close when tapped. Scatter the mussels over the rice, put the lid on the pan and simmer for an extra 4–5 minutes.
Check that the mussles have opened. Discard any mussels that remain closed.
Fold the dill into the rice and mussels before serving.