In a small bowl, whisk together the Cajun seasoning, brown sugar, and salt. Set a plate and a large piece of aluminum foil aside.
Place the chicken and shrimp in two separate medium bowls. Drizzle each with 1 tablespoon of olive oil, then sprinkle the Cajun seasoning blend over and toss to evenly coat all of the pieces. Cover the bowl with plastic wrap and place it in the refrigerator, allowing it to marinate for 2-24 hours.
When ready to cook, preheat the oven to 350°F. Melt 3 tablespoons of butter with 1 tablespoon olive oil in a skillet set over medium-high heat. Stir in the garlic and sauté until fragrant, about 30 seconds.
Add the shrimp and cook for 1-3 minutes per side, or until seared and opaque. Remove the shrimp from the skillet, place on the plate, and tent with foil to keep warm.
Wipe out the skillet and melt the remaining butter and oil together. Sear the chicken for 2-3 minutes on each side, then place the skillet in the preheated oven and cook until internal temperature reaches 165°F, about 12-18 minutes.
Transfer the chicken and shrimp with the remaining garlic butter sauce to a serving plate. Garnish with parsley and serve with more garlic butter.
