Preheat the oven to 400 degrees F.
Season the chicken with the basil, salt and pepper. Heat an oven safe (cast iron or enamel) pot or skillet over medium-high heat and add the olive oil. Add the chicken and sear it on both sides until it's golden brown, about 2 minutes per side. Remove the chicken and set it aside on a plate. Reduce the heat to medium and add the butter.
Add in the shallots and garlic with a pinch of salt. Stir well and cook for about 5 minutes. Stir in the peaches. Cook for another 5 minutes. Add in the peach preserves, wine and sherry, stirring with a wooden spoon to combine everything. Bring the mixture to a simmer. Once simmering, add the chicken back in. Place the pot in the oven for 20 minutes.
Remove the chicken and sprinkle with the chopped basil. Serve the chicken with a spoon for the extra sauce. You can serve this with rice, potatoes, quinoa, grilled bread, you favorite salad - the options are endless!