Cook the chicken: Melt 1 tablespoon of the butter in a medium (about 10-inch) oven-safe skillet over medium heat. Season the chicken tenderloins all over with 1 teaspoon of salt and ¼ teaspoon of pepper. Add the chicken in a single even layer to the skillet. Cook, turning as needed, until lightly browned, about 6 minutes total. Remove from skillet, place on a plate, and set aside. It’s okay if they are not cooked through—they will finish cooking later. Do not wipe the skillet clean.

Preheat the broiler: Preheat the oven to broil with a rack about 6 inches away from the heat source.

Cook the onions: In the same skillet, melt the remaining 4 tablespoons of butter over medium-high heat. Add the onions and sugar and cook, stirring often, until the onions are softened and lightly golden, about 10 minutes.

Make the sauce: Add the flour and cook, stirring constantly, for 1 minute. Gradually whisk in the broth and Worcestershire sauce until smooth. Stir in the thyme and remaining ½ teaspoon each salt and pepper.

Finish cooking the chicken: Return the chicken to the skillet in an even layer and bring the sauce to a simmer over medium-high heat. Cook, stirring and turning the chicken often, until the sauce is thickened and a thermometer inserted into the thickest portion of chicken registers 165°F, about 2 minutes. Remove from the heat.

Broil and serve: Sprinkle the top with cheese. Broil in the preheated oven until cheese is melted, 3 to 5 minutes. Garnish with additional pepper and thyme and serve. Love the recipe? Leave us stars and a comment below!