Use a thin, sharp knife to slice each chicken breast in half lengthwise to create two thin fillets. Place the chicken breasts between two pieces of plastic wrap on a cutting board, and gently pound to about ⅜-inch with a meat tenderizer.

Add the flour to a shallow bowl. In another bowl, whisk the eggs with the milk, and season with the salt and pepper. Add the panko to another shallow bowl.

One at a time, lightly dredge the chicken breasts first in the flour, then the egg mixture, and then in the panko crumbs, shaking off excess, and place on a wire rack. Repeat with the remaining chicken breasts.

Heat 2 tablespoons of oil in a heavy skillet over medium-high. Fry the chicken in batches until golden brown and crispy, about 5 minutes on each side. Add 1 tablespoon of oil to the pan and repeat with the remaining chicken breasts.

In a medium bowl, whisk together the vinegar, olive oil, ½ teaspoon kosher salt, and freshly ground black pepper. Add the shallots and tomatoes and toss to coat. Toss with the arugula and basil. Top the chicken with the arugula salad and serve with lemon wedges.