PREP: Follow package directions to thaw 1 sheet of puff pastry dough. Preheat the oven to 350 degrees F. Generously grease a glass 9- or 10-inch pie pan with nonstick cooking spray and set aside.
CARROTS & ONION: Add 2 tablespoons butter to a large pot over medium-high heat. Once melted, add the diced onion and carrots. Saute, stirring occasionally, until veggies are tender, about 10 minutes. They won't get too much more tender throughout cooking so take your time here. Add garlic, saute for another minute or until fragrant.
ROUX: Press veggies to the edges of the pot and add remaining 2 tablespoons butter into the center of the pot. Once melted, add in the flour. Cook, stirring constantly for 30 seconds to a minute. Gradually pour in the milk while stirring constantly. Cook until slightly thickened and add in the seasonings -- paprika, ground mustard, thyme, chicken bouillon powder, and salt & pepper to taste (I add 1 teaspoon salt & 1/2 teaspoon pepper, but you may want less depending on how salty Parmesan cheese is). Mix in seasonings. Sauce should be thick enough to coat the back of a wooden spoon.
ADD REMAINING INGREDIENTS: Stir in the finely diced broccoli and chopped rotisserie chicken. Mix to heat through, about 1-2 minutes. (See Note 4) Remove pot from heat. Stir in Parmesan cheese and 1/2 cup of the sharp Cheddar cheese. Gently stir until melted. Transfer contents of the pot into prepared pie pan. Sprinkle the remaining 1/2 cup Cheddar cheese on top.
BAKE POT PIE: In a small bowl, whisk the egg with a fork until smooth. Using a pastry brush, brush egg wash around the edges of the pie tin. Place thawed puff pastry on top of the pie and gently press down around corners. Generously brush the entire puff pastry with egg wash. Use a knife to cut several vents in the top. Place pot pie on a baking sheet and bake for 35-45 minutes or until deeply golden on top and pot pie is bubbling at the edges. Remove and let stand for 5 minutes before serving. Serve with fresh thyme if desired. Enjoy!
Note 1: Veggies: This is about 1 large yellow onion and 2 large carrots. Finely dice the veggies and take your time to sufficiently sauté them. The veggies won't soften much more after the initial sautéing so be sure they are all fork tender before adding butter and flour. To ensure tender veggies that don't take too long to get tender, be sure to finely dice the veggies into small and even-sized pieces.Note 2: Cheese: Store-bought Parmesan is very salty and won't melt as nicely in this recipe. We highly recommend grabbing a block of Parmesan cheese and grating it on the large holes of the grater. Grab a block of sharp Cheddar and grate it on the large holes as well, then measure. Pre-grated cheese contains preservatives that keep the shreds from clumping together in the bag, but they also keep the cheese from melting smoothly and will cause a greasy pot pie.Note 3: Puff Pastry: The puff pastry I recommend in this recipe can be found in the freezer section of your grocery store. It’s a little tricky to find sometimes, so use a store app if your grocery store has one. We love and recommend Pepperidge Farm® puff pastry sheets. There are 2 sheets per package and we only use one for this recipe. Set out one to thaw and then tightly wrap up the other one and promptly return it to the freezer.Note4: Filling: Before taking the filling off the stovetop, make sure it is thickened to your desired consistency. It will thicken a bit more with the cheese, but doesn't thicken much once the puff pastry is added on, so if needed, keep cooking until you have a nice and creamy consistency -- it should not be watery or the pot pie will end up watery! On the other end of the spectrum, if filling ends up overly thickened, you may want to add a splash more of milk.STORAGE: Once made this pot pie is best enjoyed promptly. Leftovers store okay, but the puff pastry definitely softens and loses texture. Cover leftovers and keep in the fridge for 3-4 days. Reheat in the oven at 350 degrees F, covered with foil for about 20-25 minutes. To prepare ahead of time, make the filling right up to the point of adding the puff pastry on top; instead, let it cool completely to room temperature. Cover the cooled filling in the pie pan and refrigerate. When ready to assemble, top with thawed puff pastry dough and bake. You may need to add an additional 10-15 minutes added to bake time since the filling is chilled. Cover pot pie with foil if the pastry dough is overly browning.