Use paper towels/kitchen roll to pat the cod fillets dry to remove excess moisture. In a large shallow dish, combine the flour, salt and white pepper. One by one, dredge the fillets in the flour, give them a shake, then place to one side.
In a large non-stick pan over medium-high heat, add 1 tbsp oil and butter. Once the butter has melted and the pan is hot, space out the fillets. Fry for 2-3 minutes on each side, or until golden on the outside and just about opaque through the centre. Carefully remove the fillets and place them on a plate to one side. Timings will depend on the thickness of the fillets, but I recommend being cautious as the cod will carry on slightly as it rests and when added back to the pan.
Lower the heat to medium and melt the 2nd tbsp of butter. Add the shallots and parsley stalks and gently fry until soft and golden. Add the garlic and fry for 30 seconds or so longer, then stir in the stock and cream. Stir in the mustard, lemon juice and most of the parsley leaves (save some to garnish), then bring to a simmer.
Simmer for around 3-5 minutes, stirring somewhat frequently, until the sauce thickens. Stir in the resting juices from the cod and adjust seasoning (generously if needed) with salt and pepper. Add the cod in the pan and baste in the sauce to gently warm it back through if needed, then serve with extra parsley and a lemon wedge. Enjoy!