Heat oil in a large skillet over medium heat. Add onion and garlic and cook for 3 minutes, or until softened. Add mushrooms and peas and cook for 5 minutes more.
Add chicken and cook for another 3 minutes. Sprinkle flour over the mixture and stir to combine. Add broth, thyme, oregano, salt, and pepper and stir until thickened, about 3 minutes.
Remove from heat and stir in sour cream. Pour mixture into a 9-inch pie plate.
Roll out pastry dough and place over the top of the filling. Trim off any excess dough and crimp edges with a fork.
Bake in preheated oven for 25 minutes, or until golden brown.
Interesting Facts
Chicken pot pie is an American classic that dates back to the 19th century.
The origin of the dish is unclear, but it is believed to be derived from a British dish called "potted meat pie".
The dish is also popular in Canada, where it is sometimes referred to as "Canadian pot pie".