Preheat oven to 400°F.
Roll out one pie crust and place in a 9-inch pie dish. Set aside.
In a large skillet, heat the olive oil over medium heat. Add the onion, carrots, celery, mushrooms, garlic, and thyme. Cook for 8-10 minutes, until vegetables are tender.
Sprinkle the flour over the vegetables and stir to coat. Cook for 2 minutes.
Gradually whisk in the vegetable broth and bring to a simmer. Cook for 5 minutes, until thickened.
Remove from heat and stir in the peas and corn. Season with salt and pepper.
Pour the filling into the prepared pie crust. Roll out the remaining pie crust and place on top. Crimp the edges to seal.
Cut a few slits in the top crust to allow steam to escape.
Bake for 30-35 minutes, until the crust is golden brown.
Let cool for 10 minutes before serving.
