This will take you right back to the streets of New York! Place potatoes into a pot with enough water to cover. Bring to a boil, and cook until tender. Drain, and set aside. While the potatoes are boiling, heat 1/4 cup butter in a large skillet over medium heat. Stir in onions, and cook until soft and translucent.
Preheat oven to 375 degrees F (190 degrees C). Grease a baking sheet. Layer 3 sheets of phyllo dough one on top of the other, and cut this triple-layered sheet in half. Drop one spoonful of potato mixture into each phyllo piece. Roll dough around mixture, tucking ends under. Repeat this step with remaining sheets of phyllo dough to make 12 knishes.
And they even have vegan ones! At one time, knisheries could be found all over the city, from Coney Island in Brooklyn to Forest Hills in Queens. Even though they never made it as big as bagels, knishes are a quintessential New York food.
Squish down the top and tuck everything into the center to form a round knish. Repeat with remaining dough and filling. Brush bottoms with olive oil and place on the prepared baking sheets. Brush leftover egg wash on top. Bake in the preheated oven until lightly golden-brown, about 40 minutes. Let cool until just warm or room-temperature.