Step 1

Preheat the oven to 400 F and prepare a rimmed baking sheet with parchment paper or foil.

Step 2

Melt butter and oil in a large cast-iron skillet (10 to 12 inches) over medium heat. Once hot, add the onion, fennel, celery, garlic and thyme sprigs. Season with kosher salt and pepper and cook, stirring occasionally, until veggies are softened and slightly caramelized, about 7 to 8 minutes.

Step 3

Remove thyme sprigs from the pan and set aside. Dust the vegetables with flour and stir to coat. Continue cooking and stirring for 2 to 3 minutes more, or until the flour starts to look golden.

Step 4

Add the chicken stock, 1 cup at a time, stirring in between each addition to make sure there are no clumps of flour remaining. Stir in the kale, and bring to a simmer. Cook for 2 to 3 minutes to thicken.

Step 5

Reduce the heat to low and stir in the cooked chicken and peas. Add in minced fennel fronds. Season with salt and pepper to taste. It's important to season the mixture at this stage before covering with the puff pastry and baking.

Step 6

Unroll the thawed puff pastry dough and dust with flour. Use a rolling pin to flatten any seams. Working quickly, place the rolled-out dough over the skillet, leaving a 1-inch overhang and press to seal the dough to the skillet. Use kitchen shears to cut away any excess dough.

Step 7

In a small bowl, whisk together the egg and 1 tablespoon of water. Brush the top of the pastry with egg wash to add shine.

Step 8

Using a sharp knife, cut 3 to 4 slits in the top of the dough (about 1-inch long each) to vent. Sprinkle the top of the dough with flaky salt.

Step 9

Bake the chicken pot pie on a rimmed baking sheet in the oven on the middle rack for 25 to 30 minutes, or until the pastry is golden and the filling is bubbling. Check halfway through cooking and if the top is browning too quickly, tent with foil for the remainder of the cooking time.

Step 10

When the chicken pot pie is done, allow to cool for at least 10 minutes before serving.