Add potatoes to a large pot cover with enough water to cover by at least 1-inch, season with salt. Bring to a boil over high heat and then reduce to medium, let cook for 12 – 15 minutes or until potatoes are tender. Drain and transfer back to the pot. Mash potatoes until smooth, season with salt and pepper.
Meanwhile rinse the salt haddock thoroughly under warm water to remove excess salt. Add haddock to a small pot, cover with water and boil for 2-3 minutes. Drain boiled haddock and rinse again with warm water.
Crumble haddock into small pieces directly on top of the mashed potatoes. Add the shallots and herbs, season with salt and pepper. While the mixture is still warm form into 2 ½-inch wide cakes. Place cakes on a parchment paper lined baking tray. Cover tray with plastic wrap and refrigerate until cold.
Once cakes are cold. Melt butter and oil in a large non-stick pan over medium high heat, fry cakes until golden, 3 – 4 minutes per side. Transfer to another parchment paper lined baking tray.
Fried cakes can be kept warm in a 275°F oven, while remaining cakes are fried.
Once cakes have been formed, cakes can be refrigerated up to 3 days before cooking.