Heat a large sauté pan over high heat and add the oil. Season both sides of the chicken with salt and pepper, to taste. Sear the chicken, skin side down, 4 to 5 minutes. Reduce the heat to medium, flip the chicken, cover the pan and cook on second side for 7 to 8 minutes. Add the wine, 1 minced garlic clove, and herbs and continue to cook until the liquid is reduced by half. Transfer chicken to serving platter and remove the pan from the heat. Whisk in the butter, scraping up the bits from the bottom of the pan which will make the sauce for serving after.
Using a box grater, shred the potato, zucchini and squash, and add them to a large bowl. Stir in the onion, egg, flour, remaining garlic, herbs, and Cajun spice. Blend well. Add more flour if mixture is too wet. The mixture should hold its shape when squeezed. Heat a large sauté pan over medium heat. Add 2 tbsp. grape-seed oil. Portion the hash into 1/3 cup patties which should make 7-10 patties. Cook until golden brown, about 2 to 3 minutes, then flip and cook until other side is browned. Remove them from a pan to paper towel and season with salt, to taste.
Serve the chicken with Potato-Vegetable Hash and the pan sauce. Garnish with chives.
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