Bring the milk, chicken broth, thyme sprigs, bouillon powder, and chicken breasts to a simmer in a medium saucepan over medium-low heat. Cover with a lid and poach for 15 minutes, making sure to not let the liquid boil.
Remove the poached chicken from the liquid and set it aside to cool; cut it into bite-sized pieces.
Heat the butter in a large skillet over medium heat. Add the onion and cook, stirring occasionally, for 3 minutes. Add the carrots and celery and cook, stirring occasionally, for 2 minutes. Add the garlic and cook, stirring constantly, for 1 minute.
Add the wine and cook, stirring often, until evaporated. Add the flour and stir for 1 minute.
Add half of the poaching liquid through a fine sieve strainer and whisk until well combined. Add remaining poaching liquid (through a fine sieve strainer) along with the parmesan cheese and whisk until combined and thickened. Season with sea salt and freshly cracked pepper to taste.
Stir in the chicken. Pour into a baking dish that has been coated with butter and place into the refrigerator to cool for 20-30 minutes. Side Note: DON'T skip this step. A hot filling will melt the butter in the puff pastry.
Meanwhile, remove the puff pastry from the freezer to thaw.
Preheat the oven to 350 degrees.
Brush the top edge of the baking dish with egg. Top with puff pastry and either drape over the baking dish or fold down the edges & crimp, if desired.
Brush the pastry with egg and make a small slit with a knife on the top for venting.
Bake for 35-40 minutes or until golden brown. Serve immediately. Enjoy.