Combine flour and a pinch of salt in a large bowl and make a well in the center. Add 1⁄2 cup water and 1 tbsp. of the oil to the well, then, using a large spoon, gradually stir flour into liquid until dough forms a rough ball. Turn dough out onto a lightly floured surface and knead until smooth, about 15 minutes. Transfer to a clean bowl, cover with plastic wrap, and set aside for 30 minutes.
Meanwhile, put potatoes into a large pot, cover with cold water, and bring to a boil over high heat. Reduce heat to medium and cook until soft, about 30 minutes. Drain, then transfer to a large bowl. Heat about two-thirds of the remaining oil in a large skillet over medium heat. Add onions and cook, stirring often, until soft, about 20 minutes. Transfer to bowl with potatoes and mash with a potato masher until potatoes are no longer lumpy. Season to taste with salt and pepper and set filling aside.
Preheat oven to 375°. Line a large baking sheet with waxed or parchment paper and set aside. Combine egg and 1 tbsp. water in a small bowl and set egg wash aside.
Divide dough into 12 pieces, then shape each into a ball. Make one knish at a time, keeping remaining dough covered with plastic wrap to prevent it from drying out. To make each knish, roll out dough ball on a lightly floured surface into a 7" circle. Brush surface of dough with some of the remaining oil. Mound about 1 cup of the filling in center of dough and fold dough up and around sides, leaving top of filling exposed but overlapping edges of dough slightly to make a snug fit around filling. Transfer knishes, as finished, to baking sheet, brush tops with egg wash, and bake until lightly golden, 25-30 minutes.