Prepare rice in boiling salted water according to package instructions. Peel carrots and cut into small cubes. Add the carrots to the rice about 5 minutes before the end of the cooking time and cook with them.
Mix eggs and milk, season with salt and nutmeg. Wash the parsley and chop the leaves. Drain rice and carrots. Add peas and 3/4 of the parsley and mix. Grate cheese.
Put the rice mix and ham in a greased casserole dish and pour the egg milk over it. Sprinkle cheese over it and bake in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) for 30-40 minutes.
If the surface becomes too dark, cover with aluminium foil. Remove the casserole from the oven and sprinkle with the remaining parsley.