Rinse zucchini and slice off stem and a small 1" piece of the other end.
If using a spiralizer, cut a small slit lengthwise in the zucchini (this shortens the strands so they aren't super long) and place into spiral slicer.
Slice into "noodles" and place into a medium-size bowl.
If you don't have a spiral slicer, you can use a vegetable peeler and cut into ribbons or a julienne slicer and slice into tiny strips.
Bring about 3 inches of water to a boil in a pot with a steamer basket.
While water begins to boil, prepare the chicken.
Heat oil in a large, non-stick skillet over medium-high heat.
Add chicken and cook for about 5 minutes, flipping once until each side is lightly golden.
Remove chicken from pan and set aside.
Add your vegetables to the pan and add 1-2 tbsp water or chicken broth to deglaze the pan, you want to scrape up all those tasty bits of flavor from browning the chicken.
Cook vegetables until soft and water has evaporated, about 5 minutes or so.
Add zucchini noodles to the steamer basket over the boiling water and cook 2 minutes (don't overcook or "noodles" will get too soft.)
While zucchini noodles steam, add skillet sauce to the vegetables and stir to mix.
Add chicken breasts back to pan and stir well to coat.
Reduce heat to low, cover and simmer for 3-5 minutes until sauce has slightly thicken and flavors have mingled.
Drain zucchini really well and toss in melted butter.
Place parmesan cheese into a food processor and chop until resembling coarse bread crumbs.
Toss buttery noodles in parmesan cheese and spoon into a serving dish.
Season with sea salt and pepper and sprinkle with fresh parsley.
Serve alongside skillet chicken and enjoy.