Preheat the oven to 200 degrees Celsius (400 degrees Fahrenheit).
Toss the halved baby potatoes with olive oil, dried oregano, salt, and pepper on a large rimmed baking sheet.
Roast the potatoes in the preheated oven for 20 minutes until they begin to soften and brown.
In a small mixing bowl, whisk together the heavy cream, lemon juice, lemon zest, minced garlic, parsley, and dill.
Remove the baking sheet from the oven and move the potatoes to the outer edges to create space in the center.
Place the cod fillets in the center of the baking sheet and pour the cream mixture evenly over the fish.
Return the tray to the oven and bake for 12 to 15 minutes, or until the cod is opaque and flakes easily with a fork.