Add the oil to a deep nonstick skillet set over medium-high heat. Preheat while you prepare the rest of your ingredients.
Season the chicken with salt and black pepper. Dredge the chicken in the flour, then the egg, and then the bread crumbs. Place the chicken in the hot oil and pan-fry for 5-6 minutes on each side or until brown and crispy and fully cooked through. Remove from heat and set aside on a plate that has been lined with a paper towel.
While your chicken is cooking, prepare your salad. Whisk together the extra virgin olive oil, red wine vinegar, and shallot. Add the cherries and arugula. Toss to coat and then season with salt and black pepper.
Serve the chicken topped with the cherry and arugula salad. Season with additional black pepper and some flaky or coarse sea salt. Enjoy immediately!