Roll puff pastry sheets out a flat work surface and cut into 6 to 8 circles.
Toss frozen vegetables with canola oil in a bowl and spread evenly onto a rimmed baking sheet.
Bake in the preheated oven until vegetables are golden brown, 15 to 20 minutes. Remove from oven. Keep oven on. Line a shallow baking pan with aluminum foil.
Heat broth and milk in a saucepan over medium heat.
Melt 1 tablespoon butter in a saucepan over medium heat. Add onion and celery; cook and stir until translucent, about 5 minutes.
Stir remaining 2 tablespoons butter into the celery mixture; cook and stir until water is evaporated, 3 to 5 minutes. Add flour and curry; mix until combined, 1 to 2 minutes. Add the hot milk mixture; whisk until thickened, 6 to 8 minutes. Add parsley, salt, and pepper. Toss in the browned vegetables and chicken. Pour into the prepared baking pan. Top with the puff pastry circles.
Bake in the preheated oven until puff pastry is browned and mixture is hot and bubbly, about 25 minutes.