Season/coat chicken thighs with half of Cajun seasoning.
Heat 1 tablespoon butter and oil in a skillet. Once hot, place seasoned chicken thigh skin side(upside) down and sear for 3-4 minutes. It should look crispy and form a golden brown crust. Flip and cook until the chicken is cooked through.
Remove chicken thighs and keep it covered.
If the brown bits in the skillet from searing chicken are not burnt and looks black, use the same pan without cleaning to make sauce( If the residue in the skillet is burnt, then scrap the burnt bit else the sauce might taste bitter).
Add remaining butter to the skillet. Saute garlic for 30 seconds, then stir in the flour. Cook flour on low heat until the raw smell is gone.
Keeping the heat low, add paprika, Italian seasoning, and remaining Cajun seasoning to the skillet. Give it a stir. Pour chicken stock, scrap the bottom of the pan to deglaze. Let it simmer for a minute.
Lower heat, add heavy cream, freshly grated parmesan. Mix and let the sauce simmer for about 5 minutes and reduce to desired thickness.
Add seared chicken back to the skillet along with any juice in the bowl. Spoon the sauce over chicken and switch of the flame.