Step 1

Preheat oven to 425°. Heat butter in a large shallow braising pot or large skillet (around 12" in diameter) over medium. Cook onion and apple, stirring often, until very soft, 8–10 minutes. Add squash, carrots, potato, daikon, and garlic and cook, stirring occasionally, until vegetables are partly tender, 12–15 minutes. Add ginger and sprinkle with curry powder and 2 Tbsp. flour; cook, stirring to coat, just until curry powder darkens, about 1 minute. Whisk broth, soy sauce, and cornstarch in a small bowl until smooth. Add broth mixture to pot and bring to a simmer, stirring often. Cook, still stirring frequently, until mixture is very thick. Taste and season with salt, if needed. Add chicken and stir to evenly distribute. The mixture will look so thick at this point that it will seem wrong. Trust us, the vegetables and chicken will release liquid as they cook under the pastry, creating a rich and just-thick-enough sauce as they do so.

Step 2

Roll out puff pastry on a lightly floured surface until large enough to cover pot with an overhang of about 1" on all sides. Drape pastry over pot and press firmly around edges to adhere. Lightly brush with egg and cut 2–3 small slits in the center so that steam can escape.

Step 3

Bake pot pie until crust is golden brown, about 18–22 minutes, then reduce oven temperature to 350° and continue to bake until filling is bubbling around the edges and crust is well browned, 40–45 minutes longer. Let sit 10 minutes before serving.