Sauté the diced bacon over medium heat until crispy. Remove the bacon from the pan and set it aside.
Add the diced vegetables (carrots, celery, onion, and shallot) to the pan and cook until softened, about 5-7 minutes.
Add the minced garlic and cook for an additional minute until fragrant.
Stir in the flour and cook for 1 minute, whisking constantly, to create a roux.
Slowly whisk in the chicken broth and milk, scraping up any browned bits from the bottom of the pan.
Bring the mixture to a simmer and cook until thickened, about 5 minutes.
Stir in the shredded chicken, cooked bacon, and frozen peas.
Preheat the oven to 400°F (200°C).
Transfer the filling to a baking dish.
Unfold the puff pastry dough and cut it into squares.
Gently place the puff pastry squares over the filling, overlapping slightly.
Brush the top of the puff pastry with milk or egg wash for a golden brown crust (optional).
Bake for 25-30 minutes, or until the puff pastry is golden brown and flaky.
Let the pot pie cool for slightly before serving.