In a small bowl, combine 1 tablespoon Cajun seasoning with 1 teaspoon black pepper. Rub this spice blend evenly over the chicken pieces.

Heat olive oil and butter in a large skillet over medium-high heat. Add the chicken and sear each side for about 3 minutes until a golden crust forms. (The chicken need not be fully cooked at this stage.) Remove the chicken from the pan and set aside.

Lower the heat slightly and add the chopped onion and minced garlic to the same skillet. Sauté for 2-3 minutes until the onion softens. Instead of whisking the flour directly, mix the 2 tablespoons of flour with a splash of chicken broth off the heat to form a smooth slurry, then stir it into the pan.

Slowly pour in the remaining chicken broth, heavy cream, and grated parmesan cheese. Stir in the remaining 1 tablespoon of Cajun seasoning. Allow the sauce to simmer over medium-low heat while you scrape up any browned bits from the pan.

Return the seared chicken to the skillet. Let it simmer in the luscious sauce for an additional 5-8 minutes until the chicken reaches an internal temperature of 165°F. Taste and adjust salt if needed. Garnish with extra parmesan and a pinch of red pepper flakes, then serve immediately.