Defrost your puff pastry overnight in the fridge. Keep the puff pastry in the fridge until you’re ready to use it.
Saute the veggies. Melt the butter in a large, oven-safe skillet or braiser over medium heat. Once the butter is melted and foamy, add in the diced onion, leek, carrots, celery, and parsnips and stir well to coat in the butter. Cook for 4-5 minutes, stirring occasionally, until the vegetables start to soften. Add in the garlic, bouillon paste, and minced herbs and cook for another minute.
Build the filling. Sprinkle the flour over the veggies and stir well. Cook for 2-3 minutes, stirring constantly, to cook out the raw flour flavor. Stir in the white wine until it’s totally absorbed, then stir in the chicken stock and bring to a simmer for 3-4 minutes. Once the sauce has thickened, stir in the heavy cream, shredded chicken, and pepper. Simmer 3-4 minutes, then season to taste with salt. Remove from the heat and set aside.
Preheat the oven to 400ºF.
Prep the garlic herb butter. In a small bowl, whisk together the egg, melted butter, thyme, and garlic and set aside.
Roll out the puff pastry. Lay the cold puff pastry out on a lightly floured work surface and roll it out to be just a bit thinner. Repeat with the second sheet and then cut both sheets into 2-inch squares.
Top and bake. Stir the frozen peas into the pot pie filling so that everything is well mixed. Lay the squares of puff pastry in an overlapping pattern over the filling. Brush with the egg/butter mixture all over and sprinkle with flaky sea salt. Bake for 30 minutes, until the top is golden and the filling is bubbling. Rest for 10 minutes before serving.