Preheat your oven to 450°F (232°C) and grease an 8×8-inch baking dish with 1 tablespoon of olive oil.
Toss the Yukon gold potatoes with 1 tablespoon of olive oil, 1 teaspoon kosher salt, and black pepper. Spread them in a single layer in the baking dish and roast for 20-25 minutes, until golden and tender.
While the potatoes are roasting, heat the butter and remaining olive oil in a medium saucepan over medium heat. Add the shallot and cook for 5 minutes until soft.
Stir in the garlic and cook for another minute.
Add the heavy cream, chicken or fish stock, rosemary sprigs, lemon zest, lemon juice, mustard, cayenne pepper, and capers. Increase the heat to medium-high and bring to a simmer.
Reduce the heat to medium-low and let the sauce thicken for about 5 minutes, stirring occasionally.
Sprinkle the cod fillets evenly with the remaining teaspoon of salt.
Once the potatoes are done roasting, remove them from the oven and nestle the cod pieces among the potatoes.
Pour the creamy rosemary sauce over the cod and potatoes, ensuring the fillets are well coated.
Return the dish to the oven and bake uncovered for an additional 10-15 minutes, or until the cod is flaky and cooked through.
Garnish with fresh parsley before serving, if desired.
