Preheat oven to 400 degrees.
In a large oven-proof skillet, heat olive oil over medium high heat. Add celery, carrots onions, garlic, and thyme. Cook until the vegetables soften, about 5 to 7 minutes, stirring occasionally.
Season with salt and pepper and then add flour. Continuously whisk until flour is well incorporated. Slowly stir in the broth and heavy cream until mixture is smooth and starts to thicken.
Add chicken and bring to a boil; simmer until thickened and chicken is heated, about 5 minutes.
Stir in frozen mixed vegetables and potatoes.
Top mixture with biscuits in an even layer and brush tops with beaten egg.
Bake until biscuits are golden brown and filling is bubbling, about 25 minutes. Serve immediately.