Cook the rice porridge: In a saucepan, combine rice, water and ½ cup of the milk. Bring to a boil, reduce to a simmer and cook until most of the liquid is absorbed. Stir in the remaining milk and simmer, stirring occasionally, until the rice is soft and creamy (about 25 minutes). Remove from heat and let cool.
Prepare the carrot mixture: While the rice cooks, peel and grate the carrots. (For a smoother casserole, boil the carrots in lightly salted water until tender and purée them.)
Combine: In a large bowl, mix the cooled rice porridge with grated or puréed carrots. Add the beaten eggs, dark syrup or sugar, salt and nutmeg/ginger. Stir to combine evenly. Taste and adjust sweetness or seasoning.
Assemble: Preheat the oven to 175 °C (350 °F). Grease a 2‑litre (2 quart) casserole dish. Pour in the carrot mixture and smooth the top. Mix the breadcrumbs with the butter (melted or softened) and sprinkle over the casserole.
Bake: Bake for 50–60 minutes until the top is golden and the casserole is set. If the top browns too quickly, cover loosely with foil. Let the porkkanalaatikko rest for 10 minutes before serving.
