For the filling:

1. Heat the olive oil over medium heat in a large, oven-proof skillet/braiser. Add in the chicken and sauté for several minutes on both sides until browned, remove and set aside as the chicken will finish cooking later. Add the onion, garlic and carrots into the pan and sauté for a few minutes more, avoiding any browning.
2. Add the flour into the pan and stir to coat the veggies completely with the flour. Allow to cook for about a minute. Pour in the white wine and lemon juice and stir to get all the browned bits off from the bottom of the pan. Reduce the heat to low and pour in the heavy cream and chicken stock. Add in the thyme and rosemary.
3. Transfer the chicken back into the sauce along with the frozen peas and corn. Stir to coat. Season with the salt and pepper. Allow the filling to simmer on low for about 5-10 minutes, or until the mixture has thickened.

For the crust:

1. Preheat your oven to 400 degrees. Gently roll out the puff pastry to fit the circumference of your pan. If you are using a round pan, you can cut the edges of the puff pastry to fit, fold them over, or let them gently hang over the side of the pan.
2. Gently lay the puff pastry on top of the prepared filling. Use a sharp knife to cut a couple air-vents in the center. In a small bowl, whisk together the egg and water and then evenly brush the top of the puff pastry with some of the egg wash. If desired, sprinkle with flakey sea salt before baking.
3. Bake for 35-40 minutes, or until the puff pastry is golden brown.