Layered pie with root vegetable filling

Ingredients:

Dough

• 2 packages of 400 g chilled dough for pie (4 layers)
• Premium flour, for dusting
• 4 tbsp unsalted butter, melted

Filling

• 2 tbsp. l. olive oil
• 8 shallots, quartered
• 3 tablespoons unsalted butter
• 2 teaspoons of sugar
• 220 g carrots, thinly sliced
• 220 g parsnips, thinly sliced
• 1 large celery root (about 0.6 kg), peeled, halved and thinly sliced
• 3 tbsp. premium flour
• 1 and 1/4 cups heavy cream
• 6 sprigs of thyme
• 2 bay leaves
• 1 teaspoon finely grated lemon zest
• Juice of half a lemon
• 5 green onions, chopped
• 2 tbsp chopped fresh parsley
• 1 large egg, lightly beaten

Preparation:

1. Dough:
   On a lightly floured work surface, roll out 2 sheets of pie dough. Brush 1 piece with half the melted butter and place the other sheet on top. Roll the 2 sheets together into a 12 x 14-inch rectangle. Repeat with the remaining 2 sheets of pie dough. Place one rectangular sheet of dough in an 8 x 11-inch baking pan, leaving an overhang on all sides. Transfer the remaining sheet of dough to another baking sheet. Refrigerate the dough until firm, about 30 minutes.
2. Prepare the filling:
   Meanwhile, heat the olive oil in a large skillet over medium heat. Add the shallots and 1 cup of water. Cook, stirring occasionally, until the liquid has evaporated and the shallots begin to darken, about 20 minutes. Add 1 tablespoon of butter and 1 teaspoon of sugar. Cook, stirring, for about 3 minutes; season with salt and pepper to taste and set aside.
3. In a large saucepan, heat the remaining 2 tablespoons butter over medium heat. Add the carrots, parsnips, celery root, and the remaining 1 teaspoon sugar. Cook, stirring, until the vegetables begin to soften, about 3 minutes. Sprinkle with flour and 1/2 teaspoon each salt and black pepper. Cook, stirring, for 2 minutes. Gradually whisk in the heavy cream and 1 cup water.
4. Tie the thyme sprigs and bay leaf into a bundle with kitchen string and add to the pan. Reduce the heat to medium and simmer, stirring occasionally, until the vegetables are tender and the liquid is thick, about 15 minutes. Let cool to room temperature. Remove the bundle. Add the lemon zest and juice, green onions, and parsley.
5. Position a rack in the upper third of the oven and preheat to 200°C (400°F). Spread the shallots evenly over the dough in the pan, then add the root vegetables in an even layer. Top with another sheet of dough; use scissors to trim off any excess dough, leaving a 2.5 cm (1 inch) overhang. Pinch the two sheets of dough together, then tuck the overhanging dough underneath. Refrigerate for 20 minutes.
6. Brush the top layer of dough with beaten egg. Using a small knife, make decorative slits in the surface of the dough, being careful not to cut all the way through; make a few holes to allow steam to escape. Bake until golden brown, about 40 minutes. Let rest for 10 minutes and serve.