Begin by cutting the chuck beef into medium-sized chunks if not already done. Place the beef chunks in a large bowl and season generously with kosher salt, black pepper, and paprika. Add 2 tablespoons of the all-purpose flour and toss again to evenly coat the beef. Heat about 2 to 3 tablespoons of olive oil in a large, deep pot or Dutch oven over medium-high heat. Working in batches, add the seasoned beef pieces and sear on all sides until deeply browned. Remove the browned beef with a slotted spoon and set aside. Repeat with any remaining beef, adding more oil if needed.

Using the same pot, add a little more olive oil if the pot seems dry. Add the chopped onion, thickly sliced carrots, celery, and parsnip, and sauté for a couple minutes until they begin to soften. Stir in the minced garlic, Italian herb blend, bay leaves, dried thyme, and ground white pepper, allowing the aromatics to cook until fragrant, about 1-2 minutes.

Stir in the tomato paste and mix well with the vegetables. Pour in the red wine to deglaze the pot, scraping up any browned bits from the bottom, and let it reduce for a few minutes. Sprinkle the remaining 3 tablespoons of all-purpose flour over the contents and stir to coat. Return the seared beef from Step 1 to the pot, then pour in the beef broth and add the baby yellow potatoes. Stir everything together and bring the mixture to a lively simmer. Reduce the heat to low and gently simmer, uncovered, for about 2 1/2 hours, stirring occasionally, until the beef is very tender and the sauce thickens. If needed, cover for the last 15-20 minutes if the sauce reduces too much. I like to check the stew occasionally to make sure it doesn't dry out—add a splash more broth or water if necessary.

Once the beef is tender and the sauce is rich, stir in the thawed petite peas, chopped fresh parsley, and fresh thyme leaves. Allow the stew to cool to room temperature. For convenience, you can prepare this filling the day before, or quickly cool it in the refrigerator. Cooling is important so the puff pastry doesn't melt before baking.

When the beef stew filling has mostly cooled, remove the puff pastry sheet from the freezer and let it thaw for 30-45 minutes, or as directed on the package. Preheat your oven to 400°F and prepare a large, deep baking dish (about 2 1/2 quarts). Transfer the cooled beef stew filling into the baking dish. Roll out the thawed puff pastry sheet to fit the dish—it can be a bit larger so you can tuck the edges in for a thicker crust. Drape the puff pastry over the filling and gently tuck the edges around the stew.

Brush the surface of the puff pastry evenly with the beaten egg yolk to create a shiny, golden crust. Use a sharp knife to make 4 slits in the pastry to allow steam to vent during baking. Bake the pot pie in the preheated oven for 30-35 minutes, or until the crust is golden-brown and beautifully puffed. I like to let the pot pie rest for 10 minutes out of the oven, as this helps the filling set a bit and makes serving easier.

To finish, sprinkle the top of the pot pie with a little extra fresh thyme leaves or parsley for a vibrant, fresh touch. Serve hot, making sure everyone gets a bit of that flaky pastry and rich, savory filling.