In a mixing bowl, combine the flour and a pinch of salt. Cut in the cold butter until the mixture resembles coarse crumbs. Gradually add ice water, stirring until a dough forms. Chill for at least 30 minutes.

Heat olive oil in a large skillet. Season chicken thighs with salt and pepper, then brown for 5-7 minutes on each side until golden. Remove and chop into bite-sized pieces.

In the same skillet, add chopped onion, diced carrots, and sliced mushrooms. Sauté over medium heat for about 5-7 minutes until softened. Add minced garlic and cook for an additional 1-2 minutes.

Sprinkle flour over the sautéed vegetables and stir for 1 minute. Gradually pour in chicken broth while stirring, bring to a simmer, and cook until slightly thickened.

Stir in heavy cream, chopped chicken, frozen peas, thyme, rosemary, and any additional seasoning. Remove from heat and let cool slightly.

Preheat your oven to 400°F. Roll out the chilled dough to fit the bottom of a pie pan. Pour the chicken filling inside, roll out a second dough piece for the top, seal edges, and cut slits for steam.

Bake the pot pie for 30-35 minutes until the crust is golden brown and the filling is bubbling. Let cool for a few minutes before serving.