Preheat a large cast iron skillet or regular frying pan over high heat and add the olive oil. Season the carrots with salt and pepper and add them to the pan. Cook over medium high heat for about 25 minutes, rotating and adjusting the heat as needed, so they get a deep black char but do not burn.
Meanwhile, in a food processor or blender, add the tahini, garlic, lemon juice, and honey. Season with a pinch of salt and pepper. Process and you will see it thicken up at first. Add a splash of the cold water and keep processing the mixture until it reaches the desired texture, adding more cold water if needed.
Pile the carrots on a plate, drizzle with the tahini, and top with the parsley and another sprinkle of salt and pepper to taste.