Preheat oven to 350 F. Heat a large ovenproof skillet over medium-high heat and add 2 tablespoons of oil. Pat the chicken dry and sprinkle with salt and pepper. Lay the breast halves, smooth-side down, in the skillet and cook, flipping once, until golden on both sides, about 4 minutes per side. Transfer the skillet to oven and bake until just cooked through, 10 to 12 minutes. Transfer the baked chicken to a cutting board to rest for 5 minutes.
Meanwhile, whisk the remaining 1/4 cup oil, parsley, vinegar, pepper flakes, garlic, 1/2 teaspoon salt and a few grinds of pepper together in a small bowl. Slice the chicken and serve with the herb oil, roasted potatoes and a green salad if desired.
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