Heat your oven to 375°F and grab a large skillet. Melt the butter over medium-high heat and add your diced chicken thighs. Sear for about 5-7 minutes until they get golden on the edges but aren't totally cooked through yet. You're not trying to cook them all the way—just get some color on them. This step makes a huge difference in the final flavor.
Push the chicken to the side and add your diced onion and carrots to the same pan. Cook for about 3 minutes, stirring occasionally, until the onion starts getting soft and smells amazing. Throw in your minced garlic and cook for another 30 seconds—don't skip this because garlic burns fast.
Sprinkle the flour over everything and stir it constantly for about 1 minute. This creates your roux, which is what thickens the whole sauce and prevents that watery mess. You'll notice the mixture gets pasty and coats the chicken and veggies completely.
Pour in your chicken broth and milk slowly while stirring constantly. Keep stirring for 2-3 minutes as the sauce thickens up—you should see it get silky smooth and coat the back of a spoon. Add your thyme, black pepper, and cubed potatoes. Bring everything to a gentle simmer.
Let it simmer for about 8-10 minutes until the potatoes are mostly tender and the chicken is fully cooked through. Stir in your frozen peas at the very end—they don't need cooking, just thawing. Taste and adjust your seasoning if needed (I usually add a pinch more pepper).
Transfer everything to a 9x13-inch baking dish and let it cool for about 5 minutes. This keeps the heat from making your pastry soggy before it even goes in the oven. Meanwhile, remove your puff pastry from the fridge so it gets a little softer and easier to handle.
Lay the puff pastry over the top of your chicken pot pie recipe filling and tuck the edges down inside the dish. It doesn't have to be perfect—honestly, rustic-looking is more appealing. Bake for 20-25 minutes until the pastry is puffed up and golden brown on top.