Mashed potatoes:

1. Mashed potatoes: Chop potatoes into smaller, evenly sized pieces. Put potatoes in a 3 quart pot and fill with cold water to cover the potatoes by 1-2 inches. Optionally add 1 tablespoon of salt to the water for seasoning.
2. Boil the mashed potatoes over medium-high heat for about 15 minutes or until a fork inserts easily into a potato. Drain the water from the potatoes and return to the warm pot.
3. Add the butter, milk, salt, and pepper to the potatoes and mash them with a hand masher or hand beaters. Taste for salt preferences.

Cheese and leek sauce:

1. Preheat the oven to 375°F. While the potatoes are cooking, start the cheese and leek sauce. Melt 1/4 cup butter in a large skillet or 3+ quart pot on the stove over medium heat. Add the sliced leeks. Cook, stirring occasionally for 15-17 minutes or until the leeks start to shrink and get some color.
2. Add the 1/4 cup of flour along with the salt and pepper. Stir to combine and let cook for 1-3 minutes. Pour the milk into the pot while whisking to incorporate it with the butter/flour roux. Turn the heat up to medium-high
3. Simmer the milk and leeks for about 5 minutes, stirring as the sauce thickens. Turn the heat off and add 4 ounces of shredded cheddar cheese, whisking to combine. Taste for salt.

Assemble the dish:

1. Put potatoes into a 3 quart casserole dish and spread them out evenly. Using the back of a spoon, create 8 to 10 divots for the eggs to nest in. Place half of an egg, yolk side up, into each divot.
2. Pour the cheese sauce over the top of the potatoes and eggs, spreading out with a spatula until evenly covered. Top with the remaining 2 ounces of shredded cheddar cheese.
3. Bake in the 375° preheated oven, uncovered, for 25 minutes, then broil for 3-5 minutes until the cheese on top starts to get brown and bubbly.