Preheat oven to 400°F (200°C). Grease a pie dish or small skillet and set aside. This is your moment to pretend you’re a fancy baker, even if you’re in sweatpants.
In a skillet, melt butter over medium heat. Sauté onion until translucent, about 3–4 minutes. Add garlic and cook 30 seconds more. It already smells like comfort, right?
Stir in flour and cook 1–2 minutes to make a light roux. This thickens things up and keeps the filling from being soupy.
Slowly whisk in milk and broth. Bring to a simmer and cook until slightly thickened, about 3–5 minutes. Stir in cream cheese, thyme, salt, and pepper until smooth.
Add chicken and vegetables. Stir until everything is evenly coated with that creamy goodness. Taste and tweak the seasoning if needed.
Roll out puff pastry or pie crust. Cover the filling, crimp edges, and cut a few slits on top to vent. If you’re feeling fancy, brush with the beaten egg for a glossy finish.
Bake 25–30 minutes, or until the crust is golden brown and the filling is bubbling. Let it rest a few minutes before serving so you don’t burn your tongue and your enthusiasm.