Combine meat, onion, and celery in a large skillet; cook until meat is browned, stirring to crumble. Drain off pan drippings. Add next 7 ingredients; reduce heat and simmer, uncovered, 5 minutes. Remove from heat; stir in potatoes, breadcrumbs, and 1 egg. Set aside, and let cool.
Cut each sheet of puff pastry into 4 equal squares. Place 2 tablespoons meat mixture on each square; brush edges of pastry with beaten egg. Fold pastry in half to form triangles; press edges together with tines of fork to seal.
Place on lightly greased baking sheets. Brush tops with beaten egg. Bake at 375° for 25 to 30 minutes or until lightly browned.