Fill a large pot 3/4ths of the way full of water and salt well. Once boiling, add the spaghetti, stirring often and cooking until al dente. Set aside about ¼ cup of pasta water. Drain the pasta and very lightly toss with some olive oil to prevent sticking. Set aside.
Toss the chicken breast with arrowroot, salt and pepper until coated.
Using a large, deep pan, heat 1 tbsp of ghee and 1 tbsp of olive oil over medium-high heat. Once melted and shimmering, add the chicken in a single layer, evenly spacing to avoid crowding so the chicken gets crispy. Once crisp on one side, rotate tongs to crisp the chicken on all sides. Set aside once cooked.
Reduce the heat and add another tablespoon of ghee. Once melted, add the garlic and shallot and saute for about a minute or until lightly fragrant.
Add the white wine, scraping the bottom of the pan to remove any browned bits. Add the broth, lemon juice and pasta water. Simmer for about 5 minutes or until the sauce is reduced.
Reduce the heat to low and add the cooked chicken, pasta, and remaining tablespoon of 2 tbsp of ghee back to the pan. Stir to coat the pasta and chicken. Add the parsley and serve fresh.