Custard egg patty: preheat oven to 300 F (150 C). 

Beat five eggs in a bowl until they are fully combined. 

Using a strainer, strain the eggs into another large bowl and add salt and milk. Mix the mixture until fully incorporated. 

IMPORTANT: spray an 8 x 4-inch loaf pan (sometimes called "Medium" - an 8.5 x 4.5 pan will also work) with nonstick spray and set the loaf pan into a larger baking pan.

Pour the egg mixture into the loaf pan. Take note of the height of the egg mixture for the next step.

Cover the loaf pan with aluminum foil and fill the larger baking pan with warm water. Make sure the water is higher than the height of the egg mixture. This is known as a bain-marie and this method of cooking the eggs surrounded by warm water will allow them to cook very gently. 

Bake for 35 to 40 minutes or until eggs are fully set. 

Allow the egg patty to fully cool before handling. See notes for reheating instructions.

Crispy hash brown patty: peel two russet potatoes and grate them with a box grater. Add the grated potatoes to a bowl and cover with water.

Let the potatoes sit in the water for 15 minutes to wash off the starch.

Scoop out the potatoes and put them in the middle of a clean kitchen towel. Pull up the sides and corners of the towel and tighten them to twist the towel around the potatoes, attempting to squeeze out as much liquid as you can.

Once the potatoes are as dry as you can get them, add them to a large pot. Cover the potatoes with oil. Bring the oil and potatoes from room temperature up to 215 degrees F (101 C). 

When that temperature is hit, immediately scoop out the potatoes and place them on a sheet pan to cool. Sprinkle with salt at this point and mix that into the soft shredded potatoes. 

After 10 or 15 minutes the potatoes should be cool enough to handle, and you can start shaping them into hash brown patties. If you want perfect shapes, you can use a large biscuit cutter. Otherwise, you should lay out a piece of parchment paper and shape the potatoes into patties that are between 3 to 4 inches in diameter and between 1/2 and 3/4-inch thick. 

Once your patties have been formed, place them in the freezer for 2 hours to fully firm up. After two hours you can cook your potatoes, or you can remove them from the parchment paper and place them in freezer-safe zip-top bags for longer storage. 

When it's time to cook the hash browns, bring about an inch of oil up to 350 degrees in a large pot or pan. Once the oil is at the proper temperature, carefully add the frozen hash brown patties, one to two at a time, and cook on the first side for around 3 minutes and then flip to cook the second side for about the same amount of time. Once both sides are golden brown and crunchy looking, remove them to a paper-towel-lined plate to cool. Immediately sprinkle with salt and black pepper (if desired) while they are still hot.

Sandwich assembly: combine the scallions, pickled onions, pickled onion liquid, and mayonnaise to create your pickled onion sandwich sauce. Store any leftover sauce in the fridge for up to a week.

Toast your bun if desired.

Add a generous spoon of pickled onion sauce to the bottom bun. Top the sauce with a crispy hash brown patty.

Using one of the reheating processes in the notes below, warm your custard egg patty and add cheese if you desire. Add the warmed egg patty on top of the hash brown.

Top the egg and cheese with 1 or 2 slices of bacon. Add a teaspoon or two of pepper jelly and another spoonful of pickled onion sauce to the top bun, completing the sandwich.

Serve and enjoy.