Preheat oven to 400 degrees Fahrenheit. If your chicken is not pre-cooked, cook and shred it into bite-sized pieces.

In a large bowl, mix 2 cups all purpose flour and 1 teaspoon salt. Cut in 3/4 cup cold butter until the mixture resembles coarse crumbs. Add 6 tablespoons cold water slowly, mixing until dough comes together. Wrap and chill in the fridge while preparing the filling.

Melt 2 tablespoons butter in a skillet over medium heat. Add chopped onion and minced garlic and cook until softened, about 3-4 minutes.

Add diced carrots and potatoes. Cook for 5 minutes, stirring occasionally. Stir in 1/4 cup flour to coat the vegetables.

Gradually add 2 cups chicken broth and 1/2 cup milk or cream while stirring. Simmer until thickened, about 7 minutes.

Stir in shredded chicken and green peas. Season with salt, pepper, and 1/2 teaspoon thyme. Cook for 3 more minutes, then remove from heat to cool slightly.

Roll out half of the dough and fit it into a 9-inch pie dish. Add the chicken filling.

Roll out the remaining dough and place on top. Seal the edges and cut a few slits in the top crust to let steam escape.

Bake for 35–40 minutes, or until the crust is golden brown. Cover edges with foil if they brown too quickly.

Let the pie rest for 10 minutes before serving.