Preheat the oven to 425 degrees F (220 degrees C).

Place 1 pie crust in a 9-inch pie plate. Poke several holes in bottom of crust.

Bake in the preheated oven for 5 minutes. Set aside to cool.

Season both sides chicken breasts with rosemary, parsley, salt, and black pepper. Heat oil in a large skillet over medium-high heat. Add chicken to the skillet; cook until golden brown, 2 to 4 minutes per side.

Reduce heat to medium-low. Add ⅔ cup chicken broth; simmer until chicken is just cooked and juices run clear, 10 to 15 minutes. Transfer chicken to a plate; rest, about 15 minutes. Reserve drippings in the skillet.

Melt butter in drippings in the skillet over medium heat. Add garlic; cook until fragrant, about 30 seconds. Add onion, salt, and black pepper; cook until translucent, about 5 minutes. Whisk in flour until mixture thickens.

Gradually add 1 ¾ cups chicken broth and milk, while whisking constantly, until mixture begins to thicken; remove from heat.

Cut chicken into bite-sized pieces; stir into broth mixture along with thawed vegetables until combined.

Transfer to the par-baked pie crust. Place remaining pie crust on top of pie; cut slits into top crust. Crimp edges to seal; decorate with tongs or a fork, if desired.