Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper. This ensures your Passover challah won't stick and bakes evenly.

In a medium saucepan, bring the water, vegetable oil, kosher salt, and sugar to a rolling boil over medium-high heat. Stir briefly to ensure the sugar dissolves completely.

Remove the saucepan from the heat and immediately pour in the matzo meal and potato starch all at once. Stir vigorously with a wooden spoon until the mixture forms a thick dough that pulls away from the sides of the pan.

Transfer the dough to the bowl of a stand mixer fitted with a paddle attachment, or a large mixing bowl. Let it cool for 5 to 10 minutes so it doesn't scramble the eggs when they are added.

Add the 4 eggs one at a time, beating well after each addition. The dough will look separated at first but will come together into a smooth, thick, and slightly sticky batter once all the eggs are incorporated.

Using wet hands to prevent sticking, shape the dough into an oblong loaf directly on the prepared baking sheet. Since this dough cannot be braided like traditional yeast dough, use a knife to gently score a braided or crosshatch pattern on top.

Brush the shaped loaf generously with the beaten egg yolk to achieve a beautiful, glossy finish.

Bake in the preheated oven for 40 to 45 minutes, or until the challah is puffed, deeply golden brown, and feels firm to the touch. Allow the bread to cool completely on a wire rack before slicing and serving at your Seder.