Preheat oven to 375 degrees.

In a large pot over medium heat, melt butter. Add in onion, garlic, celery and carrots until onion is translucent.

Add in flour and cook for 1 minute. Gradually add in chicken broth and milk stirring constantly. Bring to a boil and then reduce heat to low. Add in chicken and peas and simmer for 5 minutes.

Cut 4 circles out of the puff pastry, large enough to cover the top of each ramekin.

Divide filling among 4 ramekins and cover each ramekin with puff pastry, pulling the pastry down over the sides.

Beat egg and water together and brush over puff pastry.

Cut a small circle into the center of each puff pastry and bake for 35-40 minutes or until top is golden brown.