Cut each sheet of frozen puff pastry into 1-inch strips, 8 inches long. On a large cookie sheet, weave strips into a lattice large enough to cover each pot pie. Brush beaten egg onto each lattice square. Bake for 5 minutes, or until dough has risen and turned light golden brown. Set aside until ready to assemble pies. Leave oven on at 350 degrees F.
In a large saucepan, melt butter and then slowly add flour, stirring until consistency of peanut butter, but not brown like a roux. Slowly add cream and keep stirring. Add chicken base, garlic, and onion and stir until thickened. Add peas, carrots, nutmeg, if using, and cut up chicken. Remove from heat. Fill 4 individual oven-proof bowls with chicken mixture and then top each with a pre-cooked lattice square. Bake for 5 minutes or until bubbly. Any remaining pie filling may be frozen.