In a large saute pan over medium/low heat melt the butter. Add the leeks and garlic and saute for 3-4 minutes or until the leeks become softened. Sprinkle the flour over the leeks and stir. Cook for about a minute to cook out the flour flavor. Pour in the chicken stock and cook until the mixture begins to thicken.
Stir in the cream, salt, pepper, and tarragon. Cook for another minute or so or until the mixture thickens. Mix in the chicken, asparagus, peas, and cheese and stir until well combined. Remove from heat and set aside.
When ready to assemble the pot pie, lay out the phyllo on a dry surface and loosely cover with a tea towel. Melt the butter in the microwave.
In either a cast iron skillet or a pie plate butter the bottom generously with butter. Lay one piece of phyllo in the bottom and brush with butter. Add another piece of phyllo and brush with butter. Repeat this step until the bottom is completely covered and a nice base is formed. About 10-12 sheets of phyllo.
Put the chicken mixture over the phyllo base. And start layering the phyllo over the top using the same method as above. When you have 8-10 layers, gently tuck the excess into the dish.
Bake the pot pie in a 350 degree preheated oven for 40-45 minutes or until the top is a golden brown. Let rest for 10 minutes before serving.