Rinse chicken breasts under cold water and pat completely dry. Cut into 1 to 1.5-inch cubes, season with salt and pepper, and let rest at room temperature for 10 minutes.

Melt 2 tablespoons of butter in a large skillet over medium-high heat. Add bacon and cook for 6 to 7 minutes until crispy and golden. Remove bacon with a slotted spoon, leaving drippings in the pan.

Add chicken cubes to the same pan. Cook for 7 to 8 minutes, turning occasionally, until golden-edged and mostly cooked through. Transfer to a plate and cover loosely with foil.

Add 1 tablespoon of butter to the pan. Add mushrooms, season with black pepper, and cook undisturbed for about 10 minutes until deeply browned. Work in batches if needed to avoid steaming.

Melt the remaining tablespoon of butter. Add garlic and onion, cooking for 2 to 3 minutes until soft and translucent. Sprinkle flour over the mixture and stir well to form a roux.

Gradually pour in chicken stock while stirring to prevent lumps. Once thickened, slowly add milk, stirring until smooth. Stir in Dijon mustard and thyme. Adjust seasoning. Fold in bacon, mushrooms, and chicken.

Preheat oven to 410 degrees F. Line a 9-inch deep pie dish with parchment paper. Fit one sheet of puff pastry into the dish and poke holes with a fork. Pour in filling and spread evenly.

Lay the second pastry sheet over the filling. Press edges firmly to seal, removing air pockets. Roll the overhanging pastry inward to create a thick, decorative rim.

Whisk egg yolk and 1 tablespoon milk together. Brush generously over the top of the pie. Score a small circle in the center to allow steam to escape.

Bake at 410 degrees F for 20 minutes until the pastry puffs and turns golden. Reduce heat to 350 degrees F and bake for another 20 minutes until deeply golden brown. Rest for 15 minutes before slicing.