- Preheat the oven to 350°F. 
- Melt the butter in a large, heavy-bottomed pot over medium heat, then add the onion and garlic. Sauté for 4 to 5 minutes, until the onion is translucent and fragrant. 
- Sprinkle the flour over the onion mixture and whisk to combine. 
- Add the chicken broth 1 cup at a time, whisking constantly, then stir in the heavy cream, sage, thyme, salt, and pepper, continuing to whisk until mixture is smooth. 
- Stir in the chicken and the peas and carrots. Simmer the mixture for 5 minutes. 
- Transfer the chicken mixture to a deep pie pan or 2-quart casserole dish, then lay the crust over the top. Brush with the whisked egg, then bake for 30 minutes. 
- Remove from the oven and let cool slightly, then serve!