Creamy Vegetable Pot Pie

Preheat oven to 425°F with rack in lower third position. Heat butter and oil in a 10-inch cast-iron skillet over medium-high until butter is melted and foamy. Add mushrooms in a single layer. Cook, undisturbed, until golden brown and crispy on bottoms, about 5 minutes. Toss mushrooms; cook, stirring occasionally, until liquid releases and evaporates, about 4 minutes. Add carrots, leeks, and ½ teaspoon of the kosher salt. Cook, stirring occasionally, until carrots are just beginning to soften and leeks are tender, 6 to 8 minutes. Sprinkle evenly with flour. Cook, stirring constantly, until vegetables are fully coated and flour smells nutty and turns golden brown, about 1 minute. Add stock; bring to a boil over high. Reduce heat to medium-high. Cook, stirring occasionally, until liquid starts to thicken, about 3 minutes. Remove from heat; stir in whipping cream, crème fraîche, mustard, 2 teaspoons of the thyme, and remaining 1 teaspoon kosher salt. Set aside to cool slightly, about 5 minutes.

Meanwhile, roll pastry sheet out onto a lightly floured work surface into a 12-inch square. Cut evenly into 3 (4-inch-wide) strips. Cut each strip evenly into 6 triangles. Stir together egg and 1 tablespoon water in a small bowl.

Stir peas into warm vegetable mixture in skillet. Arrange pastry triangles in a concentric-circle pattern over mixture, leaving a slight (about ½-inch) overhang around skillet edges and slightly overlapping triangles (some vegetable mixture will still be exposed around edges). Brush pastry with egg mixture; sprinkle with flaky sea salt.

Place a baking sheet lined with aluminum foil on oven rack; place skillet on sheet. Bake in preheated oven until pastry is golden brown and filling is bubbly around edges, about 30 minutes. Remove from oven; let stand 10 minutes. Sprinkle with remaining 1 teaspoon thyme.