Preheat the oven to 400 degrees F. Spray a 12-cup muffin tin generously with the baking spray.
For the popovers: Whisk the milk, flour, eggs, vanilla and 1/2 teaspoon salt in a medium bowl until combined. Drizzle in the melted butter while whisking until combined; let the batter stand for 5 minutes. Add the baking powder; whisk the batter to combine and divide it evenly among the muffin cups (a scant 1/4 cup batter per muffin cup). Bake the popovers until puffed and browned around the edges, 20 to 25 minutes, rotating the pan about halfway through.
For the filling: While the popovers are baking, put the broth and flour into a medium saucepan and whisk until the flour is dissolved. Place the saucepan over medium heat and whisk continuously until the mixture comes to a boil; continue to whisk until the mixture is thick enough to coat the back of a spoon, 4 to 5 minutes. Reduce the heat to low and whisk in 2 tablespoons of the Parmesan, 1 teaspoon salt and 1/4 teaspoon pepper. Stir in the peas and carrots, then the chicken; cover to keep warm.
To assemble: When the popovers are done, turn them out of the pan, using a small spatula if necessary. Arrange 2 popovers on each of six plates or bowls and top with the chicken filling, dividing evenly among the popovers. Garnish with chopped parsley and sprinkle on the remaining 2 tablespoons of grated Parmesan.
Never leave a child unattended in the kitchen. Limit the child to tasks that are safe and age-appropriate.
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