Rinse the mussels in ice water, making sure the shells are clean. Set aside.
Sautee the onion and carrots in oil and butter in a Dutch oven or heavy pot, for about 8 minutes, or until soft.
Place the mussels in the same pot, and add the stock or water. Add the rice, oregano, dill, salt and pepper to the pot and bring to the boil. Reduce the heat and simmer, with the lid closed, for about 20-30 minutes, or until the rice is cooked, stirring occasionaly, and making sure there is liquid left on the bottom. Add more liquid if needed.
During the last few minutes of cooking, stir in the fresh parsely. When the rice is cooked, stir in the minced garlic and turn off the heat. The garlic will cook from the heat of the rice, and still retain some of its potency this way. Serve hot, garnished with fresh parsely.
Note: The rice will get inside the mussels as they start to open, creating stuffed mussels. Discard any mussels that haven't opened during cooking. We used to just eat those with hands, using a mouth as a tool to scoop out the meat part with the rice. But if you are really civilized, use a fork.