Preheat your oven to 200°C (390°F).
Chop the onion finely and dice the carrots and celery. Prepare the mushrooms by chopping them into small pieces.
Heat oil in a large skillet over medium heat. Add the chopped onion and cook until translucent and fragrant, about 5 minutes, filling the kitchen with a sweet aroma.
Add the diced carrots and celery to the skillet. Cook, stirring occasionally, until vegetables are slightly softened, about 5-7 minutes, and you hear a gentle sizzle.
Stir in the chopped mushrooms and cook until they release their earthy aroma and turn golden, about 5 minutes. Season with thyme, salt, and pepper to taste.
Pour in the vegetable broth and simmer until the mixture thickens slightly, about 3-4 minutes, filling the air with a savory scent. Remove from heat and let cool just a bit.
Meanwhile, roll out the puff pastry on a floured surface to about ¼ inch thickness, making it large enough to cover your baking dish with some overhang.
Transfer the vegetable filling into your baking dish, spreading it evenly with a spoon and pressing down gently to fill all gaps.
Cover the filling with the rolled-out pastry, trimming any excess. Crimp the edges with a fork or pinch with your fingers to seal the pie well. Cut a few small vents on top to allow steam to escape.
Brush the top of the crust with beaten egg using a pastry brush for a shiny, golden finish.
Bake in the preheated oven until the crust is golden and flaky, about 25-30 minutes, with bubbling filling around the edges and a delicious aroma filling your kitchen.
Remove the pie from the oven and let it rest for 10 minutes on a wire rack. This allows the filling to set, making slicing easier and neater.
Slice into portions and serve warm, enjoying the crisp crust and hearty, tender vegetables inside—perfect for cozy comfort.
