Pat the chicken thighs completely dry with paper towels. This step matters a lot. Dry chicken browns; wet chicken steams. Season both sides evenly with the salt, black pepper, and garlic powder.

Heat the olive oil in a large 12-inch skillet over medium-high heat until the oil shimmers and just begins to ripple, about 2 minutes. Add the butter and let it melt into the oil. Lay the chicken thighs flat in the pan, smooth side down, without crowding them. Cook undisturbed for 5 to 6 minutes until the bottom is deep golden brown and releases easily from the pan. Flip and cook the second side for 4 to 5 more minutes. The internal temperature should read 165 degrees F on an instant-read thermometer. Transfer the chicken to a clean plate and set aside loosely tented with foil.

Reduce the heat to medium. Add the minced garlic to the same skillet and stir for about 30 seconds until fragrant. Pour in the bourbon carefully and let it bubble for 1 minute, scraping up any browned bits stuck to the bottom of the pan with a wooden spoon. Those bits add real flavor to the sauce, so do not skip that scraping step.

Add the sliced peaches, chicken broth, brown sugar, apple cider vinegar, red pepper flakes, and thyme to the skillet. Stir everything together and bring the mixture to a gentle boil. Let the sauce cook uncovered for 6 to 8 minutes, stirring occasionally, until the peaches soften and the liquid reduces into a syrupy glaze that coats the back of a spoon. If the sauce thickens too quickly before the peaches are tender, add a splash more broth.

Nestle the seared chicken thighs back into the skillet, turning each piece to coat in the sauce. Spoon extra sauce over the tops. Let everything simmer together for 2 to 3 minutes so the chicken warms through and soaks up the flavors. Taste the sauce and adjust salt if needed.

Serve immediately over stone-ground grits or fluffy white rice, spooning plenty of the peach pan sauce over the top. A sprinkle of fresh thyme or thinly sliced green onion on top makes a nice finish.