Prepare Chicken: Slice the chicken breast into thin strips, then cut into small bite-size pieces for even cooking.
Prepare Vegetables: Peel and dice the potato into small cubes. Dice the carrot into pieces similar in size to the potato.
Cook Filling: Heat the cooking oil in a large skillet over medium heat. Add the chicken, potato, carrot, and mushrooms. Stir frequently and cook for about 7 minutes until the mushrooms release their moisture and the chicken begins turning white.
Add Peas and Seasoning: Stir in the frozen peas and water. Season with salt and black pepper. Continue cooking for another 5 minutes until the vegetables are tender and the chicken is fully cooked.
Cook Onion: In the same skillet, melt the butter over medium heat. Add the diced onion and cook for about 3 minutes until softened and fragrant.
Make Cream Sauce: Sprinkle the flour over the onions and stir constantly for 1 minute to cook out the raw flour taste. Slowly pour in the heavy cream while stirring until the sauce becomes smooth and thickened, about 3 to 5 minutes.
Combine Filling: Add the cooked chicken and vegetable mixture back into the cream sauce. Stir well until everything is evenly coated. Taste and adjust seasoning with additional salt and black pepper if needed.
Fill Baking Dishes: Spoon the creamy filling into small oven-safe ramekins or baking dishes.
Top With Pastry: Lay the puff pastry sheet over each baking dish. Press the edges gently around the rim and trim away any excess pastry.
Brush Egg Wash: Cut a small slit in the center of each pastry top to release steam. Brush the pastry with beaten egg for a shiny golden finish.
Bake Pot Pie: Bake at 350°F for 20 to 25 minutes, or until the puff pastry is deep golden brown and crisp.
Finish and Serve: Sprinkle chopped green onions over the hot pot pies before serving. Let cool slightly and serve warm.