Heat oven to 375°F and line a baking sheet with parchment paper. On a lightly floured surface, roll pie crust into a 13-inch round and cut into four 6-inch circles. (A small bowl and a butter knife work well for shaping and cutting; you’ll need to gather and reroll the dough to make four rounds.)
Spread 1/4 tsp. mustard onto half of each dough round, leaving a 1/2-inch border. Sprinkle with thyme. Layer the other half of each round with one quarter of the turkey, then top with 3 pear slices and a sprinkling of cheese.
Lightly whisk egg and water together. Brush edges of each pie with egg wash and fold to form a half moon. Use a fork to crimp and seal their edges, and a sharp knife to cut slits in their tops. Transfer pies to the baking sheet and brush tops with egg wash.
Bake pies until golden brown, turning once, about 25 minutes. Once cool enough to handle, wrap each in parchment paper or foil for packing.