In a shallow plate or shallow bowl combine Cajun seasoning, brown sugar, paprika, oregano, salt, and pepper; mix to combine.
Rub seasoning all around the chicken thighs.
Set a large skillet over medium heat; add 1 tablespoon butter and 1 tablespoon vegetable oil to heat up.
Add seasoned chicken thighs to the hot oil, smooth side down.
Cook chicken for 6 minutes.
Flip over and continue to cook for 6 to 7 more minutes or until cooked through and no longer pink. Check for doneness with instant read thermometer; chicken is done when internal temperature registers at 165˚F.
Remove chicken from skillet and set aside.
Return skillet to stove and set over medium heat.
Add remaining butter to the skillet and let it melt.
Stir in the garlic and cook for 30 seconds.
Whisk in the chicken broth and scrape up all the browned bits from the bottom of the pan.
Bring to a boil and let cook for 2 minutes, or until reduced. Whisk frequently.
Drizzle sauce over chicken thighs.
Garnish with parsley and serve.