Preheat the oven to 400°F. Melt the butter in a large skillet over medium heat. Add the onion, celery, carrots, and potato and cook 6 to 8 minutes until softened. Add the garlic and cook 30 seconds.
Sprinkle in the flour and stir 1 to 2 minutes. Slowly whisk in the chicken broth, then the cream. Simmer 5 minutes until thick enough to coat a spoon.
Stir in the chicken, peas, thyme, sage, salt, and pepper. Taste and adjust seasoning. Remove from heat and cool 5 minutes.
Divide the filling among four 12-ounce oven-safe ramekins, leaving ½ inch of space at the top.
Cut the puff pastry into four squares slightly larger than the ramekins. Drape over each, press the edges to seal, cut a steam vent, and brush with egg wash.
Place on a baking sheet and bake 20 to 25 minutes until the pastry is puffed and deep golden and the filling is bubbling. Rest 5 minutes before serving.