Preheat the oven to 400°F.
In a cast iron skillet, heat the oil over medium heat. Mix in the thyme, onions, carrots, potatoes and celery. Stir until vegetables begin to soften, around 5 minutes. Season with salt and pepper. Mix in the flour until fully incorporated. Mix in the broth and cream until smooth.
Add in the chicken and bring to a boil. Reduce heat and allow to simmer until thickened. Mix in the peas. Top with the biscuits in a even layer and brush with the beaten egg.
Bake in the preheated oven for around 25 minutes, or until the biscuits are golden brown. Serve immediately.