Preheat the oven to 350 degrees F. Spray a large baking sheet with cooking spray.
In a medium bowl, combine the cream cheese and poblanos until well incorporated. Season the filling with salt and pepper.
Unfold 1 sheet puff pastry on a lightly floured surface. Using a floured rolling pin, roll out to 1/4-inch thickness. Using a 5-inch diameter cutter, cut out 4 circles. Repeat with the remaining puff pastry sheet. Spoon 1 tablespoon cream cheese mixture in the center of each round. Brush the edge of each circle with egg wash and fold each empanada into a half moon. Crimp the edges with a fork.
Transfer the empanadas to the prepared baking sheet and brush them with the remaining egg wash. Bake until golden brown, about 30 minutes. Serve warm.