In a large mixing bowl, combine flour and a pinch of salt. Cut in cold butter until the mixture resembles coarse crumbs. Gradually add ice water, mixing until a dough forms. Shape it into a disk, wrap in plastic, and refrigerate for at least 30 minutes.

Heat olive oil in a skillet over medium-high heat. Season chicken thighs with salt and pepper, then add them to the skillet. Sear each side for about 5-7 minutes. Remove, let rest, and chop into bite-sized pieces.

In the same skillet, add more olive oil if necessary, and toss in diced onions and carrots. Sauté for 3-4 minutes until translucent. Add chopped mushrooms and cook for an additional 2-3 minutes. Incorporate minced garlic for the last minute.

Sprinkle flour over sautéed vegetables, stirring to coat evenly. Slowly stir in chicken broth, thickening over medium heat for about 5 minutes. Add heavy cream and stir until well combined.

Preheat your oven to 400°F (200°C) while filling cools slightly.

Roll out half of the chilled dough to create the base, fit it into a 9-inch pie dish. Pour in the filling, then roll out remaining dough for the top crust and seal edges.

Cut slits in the top crust to allow steam to escape. Brush the crust with a beaten egg wash for a golden finish.

Place the pot pie in the preheated oven and bake for 30-35 minutes, until the crust is golden brown.

Allow the pot pie to cool for 15-20 minutes before serving.