Preheat oven to 375°F (190°C). Grease a 12-cup muffin tin.
In a large pan, heat olive oil over medium heat. Sauté onions, carrots, and celery until softened. Add peas, corn, and chicken. Sprinkle flour over the mixture and stir until coated.
Pour in chicken broth and bring to a simmer. Cook until the sauce thickens. Stir in thyme, salt, and pepper. Remove from heat.
Cut puff pastry into squares large enough to fit into the muffin cups. Press pastry squares into the tin, leaving an overhang.
Spoon filling into each pastry cup. Fold overhanging pastry over the filling, and brush with egg wash.
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