Heat oven to 400° F.
Melt the butter in a saucepan over medium heat. Add the onion and cook for 3 minutes. Add the flour and cook, stirring constantly, for 1 minute. Still stirring, slowly add the broth. Cook until thickened, about 3 minutes. Add the peas and carrots, chicken, salt, and pepper. Remove from heat.
Cut each piecrust in half to form 4 half-circles. Spoon the chicken mixture over the bottom half of each half-circle, leaving a 1/2-inch border. Using your fingers, wet the border with water. Fold the top of each crust over the chicken to form a quarter-circle. Press to seal. Make three 1-inch slits in each top crust. Transfer to a baking sheet. Bake until golden, 15 to 18 minutes.