For pie crust in a large bowl mix together the flour, baking powder, and sea salt. Very thinly slice your butter and press it into the flour mixture creating thin flour covered flakes of butter. Slowly add your water continuously mixing together until a dough ball forms. Set the dough aside while you make the pie filling.
Chop the potato into about 1/4 inch cubes. Dice the carrots, celery, and onion. Set everything aside in a bowl.
In a large cast iron pan heat the stick of butter till melted and simmering. Slowly sprinkle in your flour whisking continuously. It may get clumpy. Continue whisking over medium heat till it begins to brown. Add your cream and continue whisking, it should be getting brown. Slowly whisk in the chicken broth and continue to whisk, it will get clumpy but trust the process it should thin out. If it doesn't you can add a little more chicken broth.
Once the roux is fully emulsified and brown add in your vegetables, sea salt, italian seasoning, and minced garlic. Mix everything together so the vegetables are coated in the roux and let cook on medium low for about 25 min, mixing occasionally so everything cooks evenly.
Add your peas and chopped cooked chicken, mix together and continue to cook for another 5 min. Smooth everything out so the top of the vegetables are flat.
Roll out the pie dough on a sheet of parchment paper to make transfer easier (you can also use premade dough) and flip on top of the vegetables.
Brush the dough with the egg cream mixture and bake at 375 for 30 min till the pie is sizzling and golden brown on top.