Mini Rotisserie Chicken Pot Pies

Preheat oven to 400 degrees F. In a large pot over medium-high heat, melt butter. Add carrot, celery, onion, garlic and thyme and cook, stirring regularly, 5 minutes, until tender and fragrant. Season with salt and pepper. Stir in flour and whisk constantly until golden brown, 3 minutes. Stir in white wine and let simmer until absorbed, about 2 minutes. Add chicken stock, stirring to combine. Bring mixture to a boil, then reduce heat to low and simmer until thickened, 6 to 8 minutes. Stir in rotisserie chicken and spinach and cook until chicken is heated through and spinach slightly wilted, 2 minutes more. Season with salt and pepper. On a floured work surface, roll out puff pastry to 1/4" thickness. Using a 10-ounce ramekin as a guide, cut out 4 circles one inch larger on all sides than the ramekin. Spoon chicken filling into four ramekins and cover each with a puff pastry circle. Using a sharp knife, cut slits across the top. In a small bowl, whisk together egg and 1 tablespoon water and brush on tops of puff pastry. Bake until pastry is puffed and golden, 15 to 18 minutes.