Sauté onion in butter over medium heat until softened, about 5 minutes.
Add garlic and carrots, then cook for 2 minutes. Sprinkle flour and mix.
Pour chicken stock and stir to dissolve the flour. Simmer for about 3 minutes. When it starts to bubble, mix in the chicken.
Add cream and peas. Simmer until the sauce is slightly thickened, for 6 to 8 minutes.
Season with salt and pepper. For more flavor, add herbs (thyme, sage, tarragon, or rosemary), spices (garlic or onion powder), or Worcestershire sauce. Add fresh parsley and turn off the heat.
Preheat oven to 400° F (204° C).
Roll out the pastry sheet on a lightly floured surface. Using a ramekin as your guide, make 6 cut-outs with ½-inch extra on the sides. Reroll the scraps or freeze them for later use.
Fill the ramekins and brush the outer edges with egg wash. Top with puff pastry and seal edges by pressing with your fingers. Make slits to release steam as it cooks.
Brush with egg wash and place on a baking sheet to catch any drippings.
Bake at 400° F (204° C) for 20 minutes. Lower to 350° F (177° C) and bake for another 10 to 20 minutes until golden brown.