Fill a large stock pot with washed potatoes, water, salt it heavily, and put it on high to boil. In a large saute pan, combine the leek slices and 1 stick of butter and cook on medium heat until soft. Set aside. I might have splashed mine with some Chardonnay...about 1/2 cup, but it's not crucial to the dish.
In a stand mixer fitted with the whisk attachment, whisk 2 eggs, the oil, and the water. Add the flour one cup at a time to combine. Scrape the dough out...it will be sticky...onto a floured surface and knead for 5 to 10 minutes dusting with flour as you knead. I usually make it to 8 minutes before I get tired of it. Cover it in saran wrap and chill it until you're ready to use it.
When the potatoes are fork tender, drain them and let cool enough to handle. Slip the skins off and discard. Mash in 2 sticks of butter, the entire head of roasted garlic, and the leeks with all of the butter they were cooked in. Season with salt and pepper. Set aside to cool completely.
Dust a work surface with flour and cut the chilled dough into thirds. Roll each third out into a general rectangular shape. It doesn't need to be perfect, but you want it somewhere between pita and tortilla thin. Place the potato mixture in a log down the center, leaving a little room at both ends.
Wrap the potato mixture in the dough, not too tightly, and pinch close the ends in a twisty fashion. Here's where it gets tricky. I mark my log with my thumb and forefinger all the way down before I commit to sectioning them out so that they will be all around the same size. When your spacing is good, you just do a sort of pinch and pulling at the same time to separate out the individual knishes.
Then you twist them off like you would wrap a taffy. The dough is stretchy. Once you get the hang of it, your next logs will go faster. Decide which end is going to be on the bottom and twist pinch it shut. Turn the knish right side up and flatten the bottom on your work surface, cupping the knish with one hand to form it's roundness. Pinch and twist the top until you're satisfied with how it looks.
Give the seam a once over, making sure that it, too, is pinched closed. Place the knish on a parchment paper lined baking sheet. Repeat until done.
Separate the egg yolks on the remaining 2 eggs and whisk them with the milk. Brush the knishes completely and bake on 350 for about 45 minutes to an hour. Voila!