Heat your largest skillet or Dutch oven (12″ or larger) and add 2 tablespoons of olive oil. Saute onions over medium heat until golden and soft, about 15 minutes.
While the onions are cooking mix the next 6 ingredients in a small bowl. Dip each piece of chicken in the bowl, coating both sides. You should have some remaining spice mix to dip the peach halves in later.
Remove the onions from the pan and set aside. Add the remaining 2 tablespoons of olive oil to the pan, turn the heat up to medium-high and add chicken skin-side down. Brown the chicken on both sides, flipping once. This will take about about 8 – 10 minutes. Add 1/2 cup white wine, bring to a boil and reduce heat to medium low. Cover and cook for 20 minutes. Remove chicken and set aside.
Dip peaches in remaining spice mix and cook cut-side down for 5 minutes until they begin to caramelize. Push the peaches to the side and return the chicken to the pan, skin-side up in a single layer. Arrange the peaches on top of the chicken. Scatter the onions over the chicken and peaches and add 1/4 cup more wine and 2 tablespoons of white balsamic vinegar. Cover and cook another 10 minutes. Remove the lid and cook another 5 minutes to reduce the sauce a bit.
Plate the chicken, peaches and sauce on a large platter or individual plates and garnish with basil and mint.