Follow the steps in order for the best result.
Preheat your oven according to the puff pastry shell package directions. Bake the shells on a baking sheet until golden brown and puffed.
While the shells are baking, heat the oil in a large skillet or pot over medium heat. Add the chopped onion and cook until softened.
Add the sliced celery and carrots to the skillet. Cook until they are lightly golden.
Incorporate the sliced bell pepper and bay leaf. Season with salt and pepper.
Stir in the butter until melted, then add the flour. Cook for about a minute, until bubbly, creating a roux.
Pour in the white wine, stirring to deglaze the pan. Gradually add the chicken broth, stirring constantly to prevent lumps. Bring to a simmer.
Season the cubed chicken with salt and pepper. Add it to the simmering broth and poach gently for about 2-3 minutes, or until partially cooked.
Stir in the asparagus, cream, and defrosted peas.
Continue to cook for an additional two minutes, then stir in the chopped tarragon.
Taste and adjust the seasoning with salt and pepper as needed.
Serve the Chicken a la King immediately in the hot baked puff pastry shells. Enjoy!