Either in a medium bowl with a hand mixer, or in a stand mixer with a whisk attachment, whip the aquafaba in a small bowl for 3 minutes until foamy.
Add the vegan butter, plant-based milk, flour, brown sugar, baking powder, salt, and turmeric. Mix in the stand mixer with a dough hook, or by hand on a clean work surface for 4-5 minutes until a smooth dough forms. Cover the bowl containing the dough with a plate and let it rest at room temperature for 30 minutes.
Meanwhile, place the potatoes in a pot and cover with water. Bring to a boil over high heat, then reduce to a simmer and cook for 15-20 minutes until fork-tender. Drain and transfer to a large bowl.
Mash the potatoes until smooth, then mix in the vegan sour cream, vegan cheddar, salt, and black pepper.
In a skillet, melt the vegan butter over medium-high heat. Add the diced onions and cook, stirring frequently, for 9-10 minutes until golden brown and soft. Add the caramelized onions to the mashed potato mixture and stir until fully combined. Let the filling cool to room temperature.
Preheat the oven to 375°F (190°C). Line a baking sheet with parchment paper. On a lightly floured surface, divide the dough and roll it out into two rectangles approximately 20x6 inches (50X15 cm).
Place a strip of filling, roughly 2 inches (5 cm) wide, along the long edge of both of the dough sheets. Roll the dough over the filling, tucking it snugly to form a log. Trim any excess dough and repeat with the remaining filling and dough.
Cut the log into 2-inch (5 cm) sections. Pinch and twist the open ends of each piece to seal, then place them seam-side down on the prepared baking sheet. Flatten each piece slightly with your hand.
Bake for 25-30 minutes until golden and firm.
Mix together egg wash ingredients in a small bowl and brush about half of it on the hot knishes. Return them to the oven for an additional 6-7 minutes until deeply golden-brown.
Brush with the remaining egg wash and transfer the knishes to a wire rack. Let cool for 10 minutes before serving.