Prepare the chicken - Slice each chicken breast into small, bite-size chunks equal in size. Transfer to a large mixing bowl and mix with 1 tablespoon of olive oil, Italian seasoning, garlic seasoning, salt, and pepper. Set aside.
Prepare remaining ingredients - Allow the chicken to rest as you mince the garlic, parsley, and spiralize your zucchini. Set these things aside and get started on cooking the chicken.
Cook the chicken - Grab a large cast-iron skillet (if you have one) and set it over medium-high heat. Add the remaining tablespoon of olive oil and one tablespoon of butter and swirl to coat the bottom of the pan. Work in batches, if needed, adding the chicken to the skillet in a single layer (avoid overcrowding). Cook the chicken on all sides until just cooked. Remove from the skillet and set aside.
Cook the zucchini - return the skillet to medium heat. Add the remaining 3 tablespoons of butter, minced garlic, parsley, and chicken broth. Allow the butter to melt and garlic to cook just until fragrant (approximately 30 seconds). Add the zucchini noodles. Mix well to combine the zucchini with the garlic butter and continue to cook just until the zucchini is warm (approximately 2 minutes of continuous tossing).
Return the chicken and assemble - Add the chicken back to the skillet and continue to cook just until the chicken is reheated, 1-2 minutes more. Sprinkle with shredded parmesan cheese, if desired, and lemon wedges for serving.