In a large skillet, heat 2 tablespoon butter over medium heat. Add the sliced leek, diced carrots, garlic powder, kosher salt and some fresh cracked black pepper. Sauté for 8–10 minutes, or until soft and just starting to caramelize.
Add the rest of the butter and sprinkle in the flour and stir for 1 minute. Slowly whisk in the chicken broth, letting it simmer until slightly thickened, about 3–4 minutes. Stir in the cream, lemon juice, basil, parsley, and a pinch of salt and pepper.
Stir in the rotisserie chicken and let the mixture simmer for another 2 minutes until everything is coated and warmed through. Taste and adjust seasoning, adding more lemon if you like it tangy.
Weave the puff pastry over the top and crimp edges around the skillet.
Whisk the egg with a splash of water and brush the top.
Bake at 400°F for 25–30 minutes, or until the puff pastry is golden and puffed. Let cool slightly before serving.