Skillet Basil-Peach Chicken Breasts

boneless chicken breasts (1 1/2 lbs)

kosher salt and fresh ground pepper

olive oil

shallot, thinly sliced

fresh grated ginger

garlic cloves, finely chopped

basil leaves, finely chopped plus more for garnish

low-sodium chicken broth

large peaches, peeled, pitted and sliced 1/4 inch thick (about 2 cups)