Preheat your oven to 400°F and line a small baking sheet with parchment paper for easy cleanup.
Peel and cube the russet potato into 1-inch pieces, then place them in a pot of cold salted water.
Bring the water to a boil and simmer the potatoes until they are completely fork-tender, approximately 15 minutes.
While the potatoes cook, rub the chicken breast with olive oil, half of the sea salt, half of the black pepper, and the chopped rosemary and thyme.
Place the chicken and the unpeeled garlic cloves on the prepared baking sheet and roast for 18-22 minutes until the chicken reaches an internal temperature of 165°F.
Drain the cooked potatoes and return them to the warm pot, mashing them thoroughly while they are still hot to ensure a smooth texture.
Remove the roasted garlic from the oven, squeeze the softened cloves out of their skins, and mash them into a paste before adding to the potatoes.
Fold the ghee, Greek yogurt, remaining sea salt, and black pepper into the potatoes, whipping until they are light and creamy.
Slice the herb-roasted chicken and serve it immediately alongside a generous portion of the buttery garlic mashed potatoes.