Preheat the oven. Set your oven to 375°F so it's ready to go when the filling is finished.
Sauté the vegetables. Heat a little extra-virgin olive oil in a large pan over medium heat. Add the shallot, carrot, and celery and cook until softened. Remove the veggies from the pan and set aside.
Make the roux. In the same pan, melt the butter. Sprinkle in the flour and stir constantly for about 1 minute until a roux forms.
Add tarragon + wine. Stir in the fresh tarragon, then pour in the white wine. Let it bubble and reduce for 1–2 minutes.
Build the sauce. Slowly whisk in the chicken broth until smooth and thickened. Pour in the heavy cream and continue whisking. Season with salt and pepper. Let the mixture simmer for about 10 minutes until it becomes a creamy sauce.
Add the chicken. Stir in the shredded rotisserie chicken and let it warm through.
Add veggies + peas. Return the sautéed veggies to the pan, along with the parsley and frozen peas. Mix everything until well combined.
Assemble the pot pie. Transfer the filling to a baking dish. Lay the cut up puff pastry over the top. Brush the surface with a beaten egg for that golden, glossy finish.
Bake. Place in the oven and bake for 30 minutes, or until the puff pastry is deeply golden and the filling is bubbling around the edges.
Serve. Let it rest for a few minutes, then dig in!