Heat oil in a large skillet over medium heat. Add the chicken and season with salt, pepper, and Italian seasoning. Cook until golden brown or no longer pink, 6 to 8 minutes per side. Transfer to a plate to let cool, then thinly slice the chicken on a cutting board or slice it using the slicing blade in a food processor.
In a large skillet over medium heat, melt butter. Add onion and saute until the onions turns soft and golden brown. Then add the garlic and mushrooms and cook for 2 more minutes. Now add the pepper and cook until mostly tender, 1 to 2 minutes. Season with salt, pepper, and Italian seasoning, then stir the shredded cheddar cheese and cook 1 minute. Stir in heavy cream and bring to a boil, then reduce heat and simmer, stirring occasionally, until thickened, about 5 minutes.
Add Zucchini Spirals, grape tomatoes and cook 2 to 3 minutes more, until noodles are tender and cheese has melted. Take care not to overcook the Zucchini. Stir in basil and remove from heat. Top with chicken, garnish with basil.
You can also shred the chicken in a food processor if you prefer smaller shreds of chicken. Try not to overcook the Zucchini as it does not taste as good when the zucchini becomes mushy.