Preheat oven to 400°F. Line a 13x18-inch rimmed baking sheet with parchment paper.

Whisk together eggs, basil (if using), salt, and pepper in a medium bowl. Add bacon and cheese; stir to combine. Coat a very large nonstick skillet with cooking spray; heat over medium heat. Add egg mixture; cook, gently folding occasionally with a spatula, until eggs reach desired scrambled consistency, about 2 minutes. Remove from heat.

On a lightly floured work surface, unfold puff pastry sheets; cut into thirds along fold lines to make 6 long rectangles. Brush edges of pastry rectangles with water. Spoon ¼ cup egg mixture onto half of each pastry rectangle, leaving a ½-inch border. Fold untopped side of pastry over filled side. Press edges together to seal using tines of a fork. Arrange pies on prepared baking sheet. Use a small knife to make a few small slits in top of each pie to allow steam to escape.

Bake until puffed and set but not yet browned, about 12 minutes (to serve immediately, bake until golden brown, about 20 minutes).

To freeze, let pies cool to room temperature on baking sheet. Place baking sheet with pies in freezer until pies are firm, about 1½ hours. Transfer pies to a freezer container or bag. Label and freeze up to 3 months.

To reheat, bake frozen hand pie(s) on a parchment-lined baking sheet in a 400°F oven until heated through and golden brown, about 12 minutes.