Preheat the oven to 375°F. Melt the butter in a large oven-safe skillet over medium heat. Add the onion, carrots, and celery and cook for 5 minutes until the vegetables begin to soften.
Stir in the shredded chicken and thyme. Sprinkle the flour over the mixture and cook for 1 minute while stirring.
Slowly pour in the chicken broth and heavy cream. Stir until the sauce thickens, about 3 minutes. Add the frozen peas and season with salt and pepper.
Remove the skillet from the heat. Arrange the biscuits on top of the filling, leaving a little space between each one so they can expand.
Bake for 18 to 22 minutes until the biscuits are golden brown and the filling is bubbling around the edges. Let the pot pie rest for 5 minutes before serving.