To start, heat olive oil and butter in a large skillet over medium heat. Once the butter is melted and the pan is shimmering, add the shallots and cook for 2 to 3 minutes until they begin to soften. Add the garlic and rosemary, stirring until fragrant—usually about 1 minute. Then, pour in the cream and season with a generous pinch of salt and pepper. Let the mixture simmer gently for 2 to 3 minutes to allow the flavors to meld.

Next, add the potatoes to the pan, ensuring they’re mostly submerged in the cream. Cover with a lid and reduce the heat to low. Let the potatoes simmer gently for 15 to 20 minutes, or until they’re fork-tender. Stir occasionally to make sure nothing sticks to the bottom of the pan and that the cream doesn’t reduce too much. If it gets too thick, add a splash of water or broth.

Once the potatoes are tender, nestle the cod fillets into the cream and potatoes. Spoon some of the sauce over the top of the fish. Cover again and let cook for 6 to 8 minutes, depending on the thickness of the fish, or until the cod is opaque and flakes easily with a fork. Taste and adjust the seasoning before serving. Garnish with fresh parsley if desired and serve hot with crusty bread, steamed greens, or a simple salad.