Preheat your oven to 400°F (200°C).
Season chicken thighs with salt and pepper.
Heat olive oil and butter in a large oven-safe skillet over medium-high heat.
Sear chicken thighs for 3-4 minutes per side until golden brown, then remove from the pan.
In the same skillet, sauté minced shallot and garlic until fragrant, about 1-2 minutes.
Stir in peach preserves, chicken broth, honey, Dijon mustard, and thyme, allowing the mixture to simmer until slightly thickened.
Return the chicken to the skillet, tucking the peach slices around the meat.
Transfer the skillet to the oven and bake for 15-20 minutes, or until the chicken is cooked through and the glaze is bubbly.
Garnish with fresh basil before serving.