Leave butter out to soften. Season pork chops with Cajun seasoning (approx. 1 tbsp per chop) and set aside.
In a pot cover potatoes with cold water, bring to a boil and simmer until fork tender.
In a bowl mix together butter, sugar, cayenne, and 2 tbsp Cajun seasoning. Spoon out onto parchment paper and roll into log. Place in freezer to harden for ten minutes, then refrigerate until use.
In a separate pot simmer half and half with garlic cloves for 10 minutes. When potatoes are cooked remove cloves from half and half, add to potatoes and mash together until smooth. Season with salt to taste.
Heat oil in pan and cook pork chops until caramelized on both sides and cooked through, approx. 5 minutes a side.
Steam green beans in the microwave as per package instructions.
Serve mashed potatoes, green beans and pork chops with liberal slices of the Cajun butter.