Place quartered potatoes in a large pot and cover with cold salted water. Bring to a boil and cook for 15-20 minutes until fork-tender. Pro tip: Start with cold water to ensure even cooking throughout the potatoes.

Drain potatoes thoroughly and return to the pot. Mash with butter, warm milk, egg yolk, and salt until smooth and creamy. Set aside. Pro tip: For ultra-smooth potatoes, pass them through a ricer before adding the dairy ingredients.

In a large skillet, melt 3 tablespoons butter over medium heat. Add diced onion, carrots, and celery. Cook for 8-10 minutes until vegetables are softened. Pro tip: Don't rush this step – properly softened vegetables create the foundation of flavor for your entire dish.

Sprinkle flour over the vegetables and stir constantly for 2 minutes to cook out the raw flour taste. Pro tip: This creates a roux that will thicken your sauce beautifully without any lumps.

Gradually whisk in milk and cream, stirring constantly to prevent lumps. Bring to a gentle simmer and cook for 3-4 minutes until thickened. Pro tip: Add the liquid slowly while whisking vigorously to create a perfectly smooth sauce.

Season with salt, pepper, fresh parsley, and dill. Remove from heat and gently fold in fish chunks and frozen peas. Pro tip: The residual heat will gently cook the fish, preventing it from becoming tough and overcooked.

Preheat oven to 400°F (200°C). Transfer the fish mixture to your prepared baking dish, spreading it evenly. Pro tip: Let the filling cool for 5 minutes before adding potatoes to prevent them from sinking into the mixture.

Spoon mashed potatoes over the filling, spreading gently with a fork. Create decorative peaks and ridges with the fork tines for beautiful browning. Pro tip: The peaks and valleys will create gorgeous golden spots when baked, making your pie look professionally made.

Bake for 25-30 minutes until the potato topping is golden brown and the filling is bubbling around the edges. Pro tip: If the potatoes brown too quickly, cover loosely with foil for the remaining cooking time.

Let rest for 10 minutes before serving to allow the filling to set properly and make serving easier. Pro tip: This resting time prevents the filling from being too liquidy when you cut into the pie.