Place sliced zucchini in a colander and place the colander over a bowl. Sprinkle with salt and allow to sit for at least 30 minutes.
Meanwhile, heat avocado oil to medium-high heat in a large skillet.
Place chicken on a plate and sprinkle on both sides with Italian seasoning, sea salt, and cayenne pepper. Add chicken to skillet, and cook over medium-high heat until cooked through, about 8 to 10 minutes per side. Remove from skillet.
Allow to cool and then chop.
Reduce heat to medium and add butter to the skillet and when it is melted scrape up the browned bits.
Add heavy cream and bring to a boil, whisking constantly. Reduce heat to medium-low.
Add garlic and Parmesan and cook until the Parmesan is melted.
Stir in chopped chicken, zucchini noodles, and parsley and cook for 2 more minutes, until warmed through.