2 tablespoons unsalted butter
1 small onion, diced
1 carrot, diced
¼ cup all-purpose flour, plus more for work surface
¼ teaspoon coarse salt, plus more to taste
Ground pepper to taste
2 cups low-sodium chicken broth
1½ cups cooked chicken (about ½ pound), cut into bite sized pieces
½ cup frozen peas
¾ teaspoon fresh thyme leaves, chopped
Half sheet frozen puff pastry, thawed
1 egg yolk
In a medium saucepan, melt butter over medium heat. Add onion and carrot and cook until onion softens, about 5 minutes. Add flour and ¼ teaspoon salt; cook, stirring frequently, until mixture is pale golden and has a nutty aroma, about 5 minutes.
Whisking constantly, add broth and bring to a boil. Stir frequently until mixture has thickened, about 8 minutes. Reduce to a simmer and continue to cook another 10 minutes.
Add chicken, peas and thyme and season with salt and pepper. Divide mixture into two 12 ounce baking dishes and refrigerate about 20 minutes, until mixture has come to room temperature.
Heat oven to 375°F. Roll pastry on a lightly floured surface to ¼-inch thickness. Cut in half. Using the tip of a sharp knife, cut four vents into the pastry.
In a small bowl, lightly beat egg yolk with one teaspoon water. Top baking dishes with pastry and brush on egg wash. Refrigerate 15 minutes. Bake until pastry is a deep golden color and juices are bubbling, about 35 minutes.