Preheat the oven to 400°F (200°C).
Prepare the cajun mixture by combining the spices, butter, and minced garlic. Set aside 1 tbsp of the cajun butter mixture to season the potatoes.
Rub the cajun butter generously over the chicken and under the skin.
Place the chicken breast side down on a cast-iron or baking sheet. Tuck the wings under the breast.
Add the potatoes to a small bowl and toss them in the cajun butter. Add the potatoes and peppers to roast with the chicken for a heartier meal.
Roast the chicken in the oven for 45-50 minutes, or until the skin is golden and crisp. Insert an instant-read thermometer into the thickest part of the breast. The thermometer should read 165°F is the chicken is fully cooked.
Let the chicken rest for 5-10 minutes before carving. Serve and enjoy!