Preheat the oven to 425°F (220°C).

In a large pot, melt butter over medium heat. Add onions, carrots, potatoes, and mixed vegetables. Cook until the vegetables are tender, about 5 minutes.

Stir in flour and cook for 1 minute. Gradually add chicken broth and milk, stirring constantly, until the mixture thickens.

Add shredded chicken, thyme, salt, and pepper. Cook for an additional 2 minutes.

Pour the chicken mixture into a 9-inch pie dish. Place the pie crust on top and seal the edges. Cut a few slits in the crust to allow steam to escape.

Bake for 25-30 minutes, or until the crust is golden brown.

Remove from the oven and let it cool for a few minutes before serving.