Step 1

Preheat oven to 425 degrees F.

Step 2

Whisk 1 1/4 cups broth and flour in a medium bowl; set aside.

Step 3

Heat oil in a 10-inch cast-iron or oven-safe nonstick skillet over medium-high heat. Add mushrooms; cook until browned, 6 to 8 minutes. Reduce heat to medium. Add onion and garlic; cook until tender, 4 to 6 minutes.

Step 4

Stir in the remaining 1/4 cup broth, scraping up any browned bits. Stir in the reserved broth-flour mixture, peas and carrots, sage, thyme, salt, and pepper. Bring to a boil, stirring constantly. Reduce heat and cook, stirring occasionally, until the vegetables are tender, about 10 minutes. Remove from heat; stir in chicken.

Step 5

Lay pie crust over the chicken mixture, folding the edges over as needed. Cut four 4-inch slits in the crust to allow steam to escape. Brush with egg white.

Step 6

Bake until the crust is golden and the filling is bubbly, 20 to 25 minutes. Let cool for 10 minutes before serving. Garnish with thyme sprigs, if desired.