Preheat the smoker grill to 225°F / 107°C with the super-smoke setting enabled.

Rub the whole chicken with 2 tablespoons olive oil, 1 lemon's zest, 2 tablespoons thyme leaves, sea salt, and cracked black pepper.

Insert the meat thermometer probe into the chicken and place the chicken on the smoker grill.

Smoke the chicken until it reaches 165°F / 74°C internally, about 150 to 180 minutes.

Remove the chicken and let it rest for 20 minutes.

Shred the rested chicken, discarding bones and skin.

Increase the smoker grill or preheat the oven to 400°F / 205°C.

Melt the butter with 2 tablespoons olive oil in a large skillet over medium heat.

Add leeks, carrots, celery, fennel, cremini mushrooms, remaining thyme, and salt to the skillet.

Cook the vegetables until softened, about 5 to 7 minutes.

Stir the garlic and all-purpose flour into the vegetables.

Cook the flour mixture for 1 minute while stirring.

Add chicken stock, Dijon mustard, heavy cream, potatoes, shredded chicken, sea salt, and cracked black pepper.

Bring the filling to a simmer and cook until the potatoes are fork-tender, about 15 to 20 minutes.

Stir frozen peas, basil leaves, and the remaining lemon zest into the filling.

Taste the filling and adjust the sea salt and cracked black pepper.

Transfer the filling evenly into one or two baking dishes.

Cover the baking dish with puff pastry and trim the excess pastry.

Beat the egg and brush it over the puff pastry.

Bake until the filling bubbles and the pastry is golden brown, about 25 to 30 minutes.