Season the chicken and shrimp separately with the Cajun seasoning.
Heat the oil in a cast-iron skillet over medium-high heat and cook the chicken for 7 to 9 minutes until browned and 165°F, then move it to a plate.
Cook the shrimp in the same skillet for 1 to 2 minutes per side until opaque and 145°F, then move them beside the chicken.
Lower the heat, melt the butter, and cook the garlic for 30 seconds before adding the broth, Worcestershire and brown sugar.
Simmer the sauce for 3 minutes until slightly reduced, then return the chicken and shrimp and turn them in the glaze for 1 minute.