Gather and measure all your ingredients.

In a medium pot, bring water to a boil and add the diced potatoes. Boil for about 15 minutes, or until tender when pierced with a fork. Drain and set aside.

In a large skillet, heat the olive oil over medium heat. Season both sides of the cod fillets with salt and pepper. Place them in the skillet and cook for about 4-5 minutes on each side, or until golden and flaky. Remove the fillets from the skillet and cover to keep warm.

In the same skillet, add the butter and minced garlic, sautéing for about 1 minute until fragrant. Then pour in the heavy cream, add the chopped rosemary, and stir well. Let the sauce simmer gently for 3-4 minutes until it thickens slightly.

Add the cooked potatoes to the sauce, gently stirring to coat them evenly. Return the cod fillets to the skillet, spooning the sauce over the fish.

Drizzle the lemon juice over the dish, season with additional salt if necessary, and let everything simmer together for another 2 minutes.

Transfer the cod and potatoes to plates, spooning extra sauce over each serving. Garnish with a sprig of rosemary if desired.