Preheat the oven to 350 degrees . In a medium pan, melt 4 tbsp. butter over medium heat. Add the onion; cook until translucent, about 5 minutes. Whisk in 1/2 cup flour; cook for 1 to 2 minutes. Whisk in the broth until smooth, then add 2 cups milk. Bring to a rapid simmer, whisking, then cook for 5 minutes; season.
Stir in the chicken, peas and carrots, and thyme. Divide among six 8-oz. ramekins or spoon into a 2-qt. baking dish.
In a bowl, whisk the remaining 1 cup flour, the baking powder and 1/2 tsp. salt. Using a pastry blender, cut the remaining 4 tbsp. butter into the flour mixture until crumbly. Add the remaining 1/2 cup milk; stir to combine.
Beat the eggs with 4 tbsp. water. Spoon the batter onto the filling; brush with the egg mixture. Bake on a foil-lined baking sheet until the tops are golden, 20 to 25 minutes. Let rest for 5 minutes.