Preheat the oven to 400 degrees F.
For the filling: Melt the butter in a large stockpot over medium heat. Add the onions, garlic, salt and thyme; sweat, stirring to prevent burning, until tender, 7 to 8 minutes. Add the flour and cook, whisking, to create a blonde roux, 4 minutes.
Slowly add the chicken stock to the pot and bring to a simmer. Then add the carrots, celery, potatoes and peas; cook until the vegetables are tender, 5 minutes.
Add the chicken and cook until the sauce has reached the desired consistency and the flavors have combined, 5 minutes. Reduce the heat to low and add the cream, Worcestershire, cayenne and black pepper; cook for another 3 minutes.
For the pot pie: Lay the puff pastry squares on a baking sheet, spaced 1 inch apart.
In a small saucepot, melt the butter with the paprika and salt. Brush the seasoned butter over the puff pastry. Transfer the baking sheet to the oven and bake until the puff pastry is golden brown, 20 minutes.
Ladle the hot pot pie filling into bowls and top each with a puff pastry square.