Bring a large pot of salted water to a boil. Add the halved or quartered baby potatoes and parboil for 8 minutes, then drain and set aside.
In a mixing bowl, whisk together 1/4 cup olive oil, soy sauce, honey, Dijon mustard, minced garlic, and a pinch of black pepper to make the marinade.
Add the chicken breasts to the marinade and toss to coat. Let them sit in the marinade for at least 10 minutes while you prepare the potatoes; longer for more flavor if desired.
Heat 2 tablespoons olive oil and 2 tablespoons butter in the 12-inch skillet over medium-high heat. Add the drained potatoes cut-side down and sear without stirring for 3–4 minutes until golden brown.
Flip the potatoes and cook another 2–3 minutes until golden all over, then remove the potatoes from the skillet and set aside.
Add the marinated chicken to the hot skillet and sear 2–3 minutes per side until golden and cooked through (internal temperature 165°F / 74°C).
Push the chicken to one side of the skillet, return the potatoes to the pan, and cook together for about 5 minutes so flavors meld. Season with salt, pepper, and red pepper flakes to taste.
Remove from heat, sprinkle with chopped fresh parsley, and serve with lemon wedges.
