Cook the Zucchini: Prepare 2 pans, one to cook the zucchini and the other to cook the spices. Cooking both ingredients can be done at the same time or one at a time.
Preheat one pan: Set the temperature to on medium low heat. Drizzle two tablespoons of olive oil and melt the butter at the same time. Distribute the zucchini in a single layer and move them around to coat them with oil and butter. Cook the zucchini for 3 minutes on each side or until browned. Move the pan from the heat if you are cooking the spices separately.
Cook the Spices: On a separate pan that is preheated on low temperature, add the garlic, salt, pepper, Cajun spice, dried parsley, paprika powder and olive oil, and cook for 2 minutes while continuously stirring. Add the spices into the pan of zucchini and gently toss to coat them. Garnish with fresh parsley and Parmesan cheese to serve.