Pat the chicken thighs dry with paper towels. Season both sides with Cajun seasoning, garlic powder, black pepper, and salt.
Lightly coat the chicken with all-purpose flour and shake off any excess. You only need a thin coating.
Heat olive oil and butter in a large skillet over medium-high heat. Add the chicken thighs and sear for 4–5 minutes per side, until golden brown. The chicken does not need to be fully cooked yet. Remove it to a plate.
Reduce the heat to medium. Add the onion to the same skillet and cook for 3–4 minutes, until softened.
Add the sun-dried tomatoes and garlic. Cook for about 30 seconds, just until fragrant.
Pour in the chicken broth and scrape the bottom of the skillet to lift up all the browned bits. Let it simmer for 1 minute.
Lower the heat, then add the heavy cream, Parmesan, Cajun seasoning, and smoked paprika if using. Stir until the sauce is smooth and creamy.
Return the chicken thighs to the skillet with any juices from the plate. Spoon some sauce over the top.
Simmer gently for 6–8 minutes, or until the chicken is cooked through and tender. The sauce should thicken slightly.
Stir in the lemon juice and parsley. Taste and adjust with more Cajun seasoning, black pepper, or salt if needed. Serve warm.