Place the potatoes in a large pot and cover with water. Bring to a boil and cook until just tender, about 15 minutes.
In a large pot, heat 2 tablespoons of olive oil. Add the chorizo and sauté until slightly crispy, about 5 minutes. Add the shallots and garlic and cook until the onions are translucent, about 5 minutes.
Add the vinho verde and fish stock, scraping up any browned bits at the bottom of the pot. Bring to a boil and reduce the liquid by half, about 15 minutes.
Lower the heat to medium and add the clams. Cover and cook until the clams open, about 3 to 4 minutes. Remove the clams and set aside. Add the parsley and butter and stir to combine.
In a large pan, heat the remaining olive oil. Season the fish fillets with salt and white pepper. Place the fillets in the pan and cook until golden brown, about 3 minutes. Flip and cook until done on the other side, about 3 minutes.
To serve, divide the potatoes and clams among 4 large shallow bowls. Add the broth. Top with a fillet of fish.
