Step 1

Preheat oven to 425°F with rack in top third position. Place water and porcini mushrooms in a small saucepan; bring to a boil over high. Remove from heat; let steep, uncovered, for 30 minutes.

Step 2

Meanwhile, toss together fresh mushrooms, oil, and 1/2 teaspoon each of the salt and pepper on a large rimmed baking sheet; spread out in an even layer. Roast until mushrooms are browned in spots, about 25 minutes, stirring after 15 minutes. Remove from oven. Reduce oven temperature to 375°F.

Step 3

Melt butter in a 10-inch cast-iron skillet over medium-high. Add carrots; cook, stirring often, until just beginning to soften, about 2 minutes. Add leek, celery, and 1/2 teaspoon of the salt; cook, stirring often, until leek slightly softens, about 2 minutes. Add herbs; cook, stirring constantly, until fragrant, about 30 seconds. Sprinkle mixture with flour; cook, stirring constantly, 1 minute. Stir in wine, scraping up any flour stuck to bottom of skillet; cook, stirring constantly, 1 minute. Using a slotted spoon, transfer porcini mushrooms to skillet, then slowly stir in porcini soaking water, leaving any grit at the bottom of the pan behind. Add 1/4 cup of the cream. Bring to a boil over medium-high. Boil, stirring often, until thickened, about 4 minutes. Remove from heat. Stir in baked mushrooms, peas, and remaining 3/4 teaspoon salt and 1/2 teaspoon pepper. Place skillet on a large rimmed baking sheet.

Step 4

Roll puff pastry out on a lightly floured work surface to a 12-inch square. Trim about 1 1/2 inches from each corner to form a rough circle. Roll pastry up onto rolling pin. Working quickly, unfurl pastry over filling in skillet. Fold excess pastry edges under then tuck inside skillet; crimp pastry. Using kitchen shears, cut four 1-inch-long slits into top of pastry. Using a pastry brush, brush top of pastry with remaining 2 teaspoons cream.

Step 5

Place baking sheet with skillet on top third position in oven, and bake at 375°F until pastry edges turn light golden, about 15 minutes. Reduce oven temperature to 350°F, and continue baking until pastry is puffed, golden, and crisp, 30 to 35 minutes. Let cool 5 minutes.