Preheat your oven to 400°F while you season the chicken thighs with salt and pepper on both sides. Heat the butter and olive oil together in your skillet over medium-high heat until the butter melts completely. Place the chicken skin-side down and sear for about 2 to 3 minutes per side, just until golden brown, then remove it from the pan and set it aside.
In that same skillet, add the diced onion and potato cubes without wiping out any of the browned bits left behind. Sauté everything for several minutes, stirring occasionally, until the potatoes start to pick up a golden color on their edges. Season with a bit more salt and pepper, then remove the mixture from the pan and set it aside with the chicken.
Melt the remaining butter in the skillet over medium heat, then add the minced garlic and let it cook for about a minute until fragrant. Pour in the honey, soy sauce, and vinegar, stirring everything together as it comes to a simmer. Lower the heat and let the sauce simmer gently for about 5 minutes until it thickens slightly.
Nestle the chicken thighs and the potato mixture back into the skillet, spooning some of that sauce right over the top of everything. Slide the skillet into your preheated oven and bake for 25 to 30 minutes, until the chicken reaches 165°F internally and the potatoes turn tender. Sprinkle the fresh parsley over the top right before serving.