Gather all ingredients.

Preheat the oven to 400 degrees F (200 degrees C). Line a sheet pan with parchment paper, and place individual pie shells on the sheet. Allow refrigerated pie crust to come to room temperature on the counter, about 15 minutes.

Place frozen vegetables into a microwave-safe dish, add water, cover, and microwave on High until hot, about 5 minutes. Drain.

Stir Boursin into vegetables until melted. Stir in cream, chicken, and black pepper; season with salt. Distribute mixture evenly among pie shells.

Using a 3-inch round biscuit cutter, cut 8 circles from refrigerated pie crust. Place a circle on top of each pie and crimp edges together. Using a sharp knife, cut two slits in the form of an "X" in the center of each top crust. Stir egg and water together in a cup until well combined; brush each pie lightly with egg wash.

Bake in the center of the preheated oven until lightly browned, about 20 to 25 minutes, or until lightly browned. Remove to cool on a rack before removing from tins, 5 to 10 minutes.

Remove foil tins from pies and serve warm.