Cook the chicken: Melt 1 tablespoon of the butter in a 10-inch cast-iron skillet over medium-high heat. Add the chicken in an even layer and season with 1 teaspoon of the salt and ¼ teaspoon of the pepper. Cook, stirring occasionally, until browned, about 5 minutes (chicken will not be fully cooked). Remove the chicken using a slotted spoon (do not wipe the skillet clean), place it on a plate, and set aside.

Cook the broccoli: Add the broccoli and ¼ cup water to the same skillet. Cover and cook over medium-high heat, undisturbed, until the broccoli is crisp-tender and bright green, about 3 minutes. Remove the broccoli using a slotted spoon (do not wipe the skillet clean), and place on the plate with the chicken.

Preheat the broiler: Arrange an oven rack about 6 inches from the heat source.

Make the sauce: Melt the remaining 3 tablespoons of butter in the skillet over medium heat, about 1 minute. Add the flour and whisk constantly for 1 minute. Gradually whisk in the milk until smooth.

Finish cooking the chicken: Stir in the chicken and broccoli and simmer over medium heat, stirring occasionally, until thickened and a thermometer inserted into the thickest portion of chicken registers 165°F, about 6 minutes.

Add cheeses and topping and broil: Remove from the heat and stir in the cream cheese, ½ cup of the cheddar, ¼ teaspoon of the salt, and the remaining ¼ teaspoon pepper until melted and fully combined, about 1 minute. Stir together the panko, oil, parsley, and remaining ¼ cup cheddar and ¼ teaspoon salt in a small bowl until combined. Sprinkle evenly over the chicken mixture. Broil in the preheated oven until golden brown, about 2 minutes. Garnish with additional parsley and serve. Love the recipe? Leave us stars and a review below!