Root Vegetable Slab Pie

Name: Root Vegetable Slab Pie
Ingredients: 2 14-ounce packages refrigerated pie dough (4 pieces); All-purpose flour, for dusting; 4 tablespoons unsalted butter, melted; 2 tablespoons extra-virgin olive oil; 8 shallots, quartered; 3 tablespoons unsalted butter; 2 teaspoons sugar; Kosher salt and freshly ground pepper; 1/2 pound carrots, thinly sliced; 1/2 pound parsnips, thinly sliced; 1 large celery root (about 1 1/4 pounds), peeled, halved and thinly sliced; 3 tablespoons all-purpose flour; 1 1/4 cups heavy cream; 6 sprigs thyme; 2 bay leaves; 1 teaspoon finely grated lemon zest; Juice of 1/2 lemon; 5 scallions, chopped; 2 tablespoons chopped fresh parsley; 1 large egg, lightly beaten