In a medium pot with cold water, put in the potatoes and make sure the water cover the potatoes completely. Season with salt. Bring to a boil over high heat. Once the water starts to boil, simmer and cook until the potatoes are fork tender, about 35 – 45 minutes.
Preheat the oven to 350˚F (177˚C).
Meanwhile, combine the cod with the lemon juice. Season with salt and pepper. Set aside.
In a medium pan over medium heat, warm up the olive oil and ½ tablespoon butter. Add the onions and carrots and cook until the onions are softened. Stir in the peas. Add the cod and cook through. While cooking the fish, break and flake 1/3 of them.
When the potatoes are ready, drain the potatoes and return them to the pot. Mashed the potatoes with a masher or big spoon until there is no lump. Stir in the milk and 2 tablespoons butter. Season with salt and pepper. Add a dash of paprika. Mix well. The mashed potatoes should be thicker than normal.
Put the fish mixture to the mashed potatoes. Add parsley. Gently mix everything together. Season with salt and pepper to your own taste. Transfer to your choice of casserole dish. Top with parmesan cheese.
Bake in the oven for 15 – 20 minutes or bake in the broiler for 2 - 4 minutes until the cheese is melted and the color is golden brown. Cool a few minutes before serving.