Preheat your oven to 200°C (400°F). Roll out one piece of pastry on a floured surface to about 0.5 cm thick, then gently lay it into a deep-dish pie pan, trimming excess edges. Chill in the fridge for 15 minutes.
Melt butter in a large skillet over medium heat until it sizzles softly. Add diced onion and sauté for 5 minutes until translucent and fragrant, stirring occasionally.
Add sliced carrots and mushrooms to the skillet. Cook for about 8 minutes, stirring often, until vegetables are tender and slightly caramelized, filling the kitchen with a savory aroma.
Stir in frozen peas and corn kernels. Pour in vegetable broth and bring to a gentle simmer for 5 minutes, allowing flavors to meld. If the mixture seems too watery, stir in cornstarch mixed with a little cold water to thicken slightly.
Transfer the vegetable mixture into the chilled pastry-lined pie pan, spreading it out evenly with a spatula. Roll out a second piece of pastry to cover the filling, then trim and crimp the edges to seal. Cut a small vent in the center to let steam escape.
Brush the top crust with beaten egg for a glossy, golden finish. Place the pie on the middle rack of the oven and bake for 35–40 minutes, until the crust is deeply golden and bubbling around the edges.
Remove the pie from the oven and let it rest for at least 10 minutes. This helps the filling set up and makes slicing easier without losing its shape.
Slice into wedges and serve warm, enjoying the flaky crust and hearty vegetable filling that bubbles invitingly. Pair with a simple green salad if desired.
