Preheat oven to 350°F In a large saucepan heat olive oil over medium-high heat. Add celery, carrot, garlic, and shallot to pan; sauté for 2 minutes. Add asparagus, onion, corn, and snow peas. Season with salt and pepper. Pour in chicken stock, ½ cup cream, and sweetened condensed milk. Add chicken and bring to a simmer.
In a small bowl stir together cornstarch and the water to create a thickening agent, then pour into pot; stir until thickened and bubbly. Stir in butter until melted. Stir in rosemary and thyme; remove from heat.
Cut puff pastry sheets in half, then set aside. Beat egg and the 1 tablespoon cream together; set aside.
Fill four individual ceramic baking dishes evenly with chicken mixture. Cover each dish with a piece of puff pastry. Pinch edges to seal and cut off excess around sides. Take a fork and poke a few holes in top of puff pastry. Brush puff pastry with egg mixture.
Bake pot pies about 35 minutes or until crust is golden brown.