Preheat oven to 450°F / 232°C.
While oven heats, combine 2 tablespoon cooking oil, soy sauce, vinegar, Italian seasoning, and ½ teaspoon honey in a square baking dish. Add chicken breast and turn to coat. Tenderize with a fork. Set aside (refrigerate if longer than 15 minutes).
Drizzle 2 tablespoon cooking oil over a large sheet pan, tipping to coat.
Scatter quartered potatoes over the sheet pan, tossing to coat in oil. Cover very tightly with foil to completely seal (use as much foil as needed).
Bake potatoes, covered, for 15 minutes.
While potatoes are cooking, whisk together 2 tablespoon olive oil, 1 teaspoon salt, garlic powder, and ¼ teaspoon black pepper. Set aside.
Heat a skillet over medium. Add a thin layer of cooking oil.
Remove chicken from marinade (discard marinade) and season with some salt and pepper.
Sear chicken breast on both sides until just golden brown, ~3 minutes per side. (The chicken should not be cooked all the way through at this point.) Transfer to a plate.
Remove potatoes from the oven. Working carefully (the pan is very hot!), remove foil and pour olive oil-garlic powder mixture over top. Stir gently to combine. Nestle chicken in potatoes.
Return pan to oven and continue cooking until potatoes are golden brown and very tender and chicken is cooked through (165°F), 10 to 15 minutes.
Make sauce by whisking together yogurt, lemon juice, mustard, 1 teaspoon honey, and a pinch of salt.
Transfer chicken to a cutting board and tent loosely with foil. Let rest for 5 minutes.
Slice chicken. Serve over potatoes with sauce on the side or drizzled over top. Enjoy!