Preheat your oven to 425°F. While it heats, cut the chicken breast into 1-inch chunks, trim the asparagus and cut into 1.5-inch pieces, mince the garlic, and zest the lemon. Measure out all your remaining ingredients so everything is ready when you start cooking—this will make the sauce-building process smooth and prevent overcooking.
Melt 2.5 tablespoons butter in a medium saucepan over medium heat. Once melted, sprinkle in 3 tablespoons cornstarch and stir constantly for about 1 minute to create a roux—this removes the raw starch taste and helps thicken the sauce evenly. Pour in half of the milk (about 7/8 cup) along with the crumbled stock cube and dried thyme, stirring continuously until the mixture thickens and becomes smooth, about 2-3 minutes. Add the remaining milk gradually while stirring to avoid lumps, then let it bubble gently for another minute to fully activate the cornstarch.
Remove the saucepan from heat and stir in the minced garlic, Dijon mustard, white pepper, and sour cream until fully combined and smooth. I like to add the sour cream off heat because the cooler temperature helps it blend in without curdling, giving you a silky, luxurious sauce. Taste and adjust seasoning as needed—remember the stock cube already contains salt, so be conservative.
In a large bowl, gently combine the raw chicken chunks, asparagus pieces, and peas with the completed sauce from Step 3, then fold in the lemon zest. Divide the filling evenly between two 8-inch baking dishes or similar-sized oven-safe bowls (or use one larger 9x13 inch dish if preferred). The filling should come up to about three-quarters full, leaving room for the pastry topping.
Remove the chilled puff pastry from the refrigerator and cut or trim it to fit your dish(es) with a slight overhang. Place the pastry over the filling and press gently around the edges to seal. Cut a small slit in the top of each pastry to allow steam to escape during baking. Brush the entire surface generously with the egg wash, then place the assembled pot pie(s) in the freezer for 15 minutes—this chill helps the pastry puff dramatically in the oven.
Transfer the chilled pot pie(s) directly from the freezer to the preheated 425°F oven and bake for 25 minutes until the pastry is deeply golden brown and crispy. I always let pot pies rest for 5 minutes after coming out of the oven—this allows the filling to set slightly so it doesn't immediately run out when you cut into it, and it gives the pastry time to firm up just enough for a perfect texture.