1. Begin by following the package directions to thaw 1 sheet of puff pastry dough. Preheat your oven to 350°F. Generously grease a glass 10-inch pie pan with cooking spray and set it aside. If you don’t have a 10-inch pan, a 9-inch pan will work just fine.
2. In a large pot, add 2 tablespoons of butter over medium-high heat. Once the butter is melted and bubbling, toss in the diced onion and carrots. Sauté these vegetables, stirring occasionally, for about 10 minutes or until they become tender and fragrant. If you’re using garlic, add it now and sauté for another minute or until it’s fragrant.
3. Now, press the veggies to the edges of the pot and add the remaining 2 tablespoons of butter into the center. Let it melt completely before adding in the flour. Stir constantly for 30 to 60 seconds until the mixture is bubbly.
4. Gradually pour in the milk, stirring continuously. Cook this mixture until it thickens slightly, making sure it's thick enough to coat the back of a wooden spoon. Once it reaches this consistency, stir in the paprika, ground mustard, thyme, chicken bouillon powder, salt, and pepper. The sauce should be creamy and flavorful.
5. Next, stir in the finely diced broccoli and chopped chicken, mixing everything until heated through, which should take about 1 to 2 minutes. Once everything is hot, remove the pot from heat.
6. Now it’s time to add the freshly grated Parmesan cheese and 1/2 cup of the sharp Cheddar cheese. Gently stir until the cheese has melted into the creamy mixture.
7. Transfer the filling into your prepared pie pan, spreading it evenly. Sprinkle the remaining 1/2 cup of Cheddar cheese on top to create a cheesy crust.
8. In a small bowl, whisk the egg with a fork until smooth. Using a pastry brush, apply the egg wash around the edges of the pie tin. Now, place the thawed puff pastry on top of the pie and gently press down around the edges to seal.
9. Generously brush the entire top of the puff pastry with the egg wash. Use a knife to cut several vents in the top to allow steam to escape during baking.
10. Place the pot pie on a baking sheet and bake for 35 to 45 minutes or until it’s deeply golden and the filling is bubbling at the edges. Once done, remove it from the oven and let it stand for about 5 minutes. Feel free to serve it with fresh thyme if desired. Enjoy your homemade Broccoli Cheddar Pot Pie!