Preheat your oven to 425 degrees F (220 degrees C).
In a large skillet or dutch oven, melt the butter over medium heat and add in the potatoes, carrots, salt, and pepper. Cook for roughly 10 minutes, until vegetables are starting to get tender.
Remove potatoes and carrots from the pan, leaving behind as much butter as possible. if there is not enough butter left, add an extra 2 Tbs.
Stir in the onion and minced garlic, let cook 2 minutes.
Add in flour, salt, and pepper, a paste will form. Gradually stir in the chicken broth and milk.
Simmer over medium-low heat until the mixture thickens, stirring occasionally, about 5 minutes.
Stir in parsley and green peas.
Pour the mixture into an unbaked pie crust. Cover with the second crust, seal the edges, and cut away any excess dough. Make several small slits in the top crust to allow steam to escape.
Bake in the preheated oven until the crust is golden brown and the filling is bubbly, about 1 hour 20 minutes, covering the crust with foil half way through so it doesn't over brown.
Let cool for 10 minutes before serving.