Slice each chicken breast in half lengthwise to make 4 thin cutlets; pat dry.
Season both sides of the chicken with the Cajun seasoning and garlic powder; add salt and pepper only if your Cajun seasoning is low in salt.
Heat the olive oil and 1 tablespoon of the butter in a large skillet over medium-high heat until hot.
Cook the chicken 4–6 minutes per side, or until an instant-read thermometer reads 165°F (74°C); transfer the cooked chicken to a plate.
Reduce heat to medium-low and add the remaining butter to the skillet.
Add the minced garlic, lemon juice, and chicken broth, scraping up any browned bits from the pan; let the sauce simmer for about 1 minute until slightly reduced.
Return the chicken to the skillet and spoon the sauce over the pieces to coat and warm through for 30–60 seconds.
Sprinkle with chopped fresh parsley if using and serve immediately.